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Highlights of 2011

Journal of Physics AMathematical and Theoretical

Cover image: Artistic impression of nontrivial cycles and stabilizer code generators on a lattice from ‘Constructions and noise threshold of topological subsystem codes’ by M Suchara et al 2011 J. Phys. A: Math. Theor. 44 155301.

Journal of Physics A: Mathematical and Theoretical

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Dear colleagues,

2011 has been another successful year for Journal of Physics A: Mathematical and Theoretical. The journal continues to have a broad audience and readers can enjoy high-quality research across theoretical and mathematical physics.

This collection of highlights displays some of the most highly rated articles published in the journal during 2011. All of these articles were chosen primarily for their high-quality science. This selection displays the broad scope of the journal and demonstrates that it is a meeting place for researchers to share mathematically rich work across different disciplines.

In 2011 we began to publish Insights: these are online, author-written news items highlighting the key achievements of recent work published in the journal to readers who might not be specialists in the field. All papers in this collection that have an associated Insight article are clearly marked.

Some of our best articles have been published as Fast Track Communications (FTCs). FTCs are short articles presenting important new developments in mathematical and theoretical physics. FTCs benefit from accelerated publication and our recommended reader service, where we will notify researchers selected by the authors when the article is published.

Each year we award up to three articles the Journal of Physics A Best Paper Prize to reward work that has excelled in novelty, achievement, potential impact and presentation. Details of the 2011 winners can be found in this brochure. Please contact the journal office to make your nominations for future awards.

This collection also shows details of the topical reviews and special issues that we have published throughout 2011. Topical reviews are commissioned by our Board Members to provide timely overviews of the current state of research in areas of great interest and activity, while special issues are collections of articles focused on contemporary areas of research, with contributions from world-class authors, and guest-edited by leading researchers.

2012 will be another strong year for the journal, with four special issues planned on Coherent states: mathematical and physical aspects; Applications of zeta functions and other spectral functions in mathematics and physics: a special issue in honour of Stuart Dowker’s 75th birthday; Quantum physics with non-Hermitian operators; and Lattice models and integrability: a special issue in honour of F Y Wu.

We hope that you enjoy this collection. We would like to thank all of our authors for choosing to submit high-quality work to the journal as well as our referees for providing constructive peer review and maintaining the quality standards of the journal. We look forward to working with you during 2012.

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Murray BatchelorEditor-in-Chief

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Editor-in-Chief M T Batchelor Australian National University, Canberra, Australia

Please do not send any manuscripts directly to our Board Members. Articles should be submitted via our website or by e-mail to [email protected].

Statistical Physics EditorM R Evans University of Edinburgh, UK

Chaotic and Complex Systems EditorA Pikovsky Universität Potsdam, Germany

Mathematical Physics EditorA Kuniba University of Tokyo, Japan

Quantum Mechanics and Quantum Information Theory EditorV Scarani National University of Singapore, Singapore

Field Theory and String Theory EditorA Tseytlin Imperial College, London, UK

Fluid and Plasma Theory EditorG Falkovich Weizmann Institute of Science, Israel

Editorial Board N Beisert ETH, Zurich, SwitzerlandE Ben-Naim Los Alamos National Laboratory, USAM V Berry University of Bristol, UKJ-S Caux Universiteit van Amsterdam, The NetherlandsM-Y Choi Seoul National University, KoreaS Coppersmith University of Wisconsin, Madison, USAB Derrida École Normale Supérieure, FranceD Dhar Tata Institute of Fundamental Research, IndiaP E Dorey University of Durham, UKJ Eisert University of Potsdam, GermanyE Elizalde CSIC, Barcelona, SpainP Fendley University of Virginia, USAO Gühne Universität Siegen, GermanyU Günther Forschungszentrum Rossendorf, Dresden, GermanyD D Holm Imperial College London, UK and Los Alamos National Laboratory, USAM Horodecki Gdansk University, PolandK Kajiwara Kyushu University, Japan

A V Kitaev Steklov Mathematical Institute, St Petersburg, RussiaG Korchemsky Université de Paris-Sud, FranceC Maes Katholieke Universiteit Leuven, BelgiumS Majumdar Université de Paris-Sud, FranceR Metzler University of Potsdam, GermanyJ A Minahan Uppsala Universitet, SwedenS Nazarenko University of Warwick, UKA M Ozorio de Almeida Centro Brasileiro de Pesquisas Fisicas, BrazilJ H H Perk Oklahoma State University, Stillwater, USAA Pumir École Normale Supérieure de Lyon, FranceP Schmelcher Universität Hamburg, GermanyP Sollich King's College London, UKR Tumulka Rutgers University, USAM Visser Victoria University of Wellington, Wellington, New ZealandA Vulpiani Università di Roma ‘La Sapienza’, ItalyY Wang Chinese Academy of Sciences, Beijing, ChinaP Wiegmann University of Chicago, USAH-Q Zhou Chongqing University, People’s Republic of China

Editorial Board

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H i g h l i g h t s o f 2 0 1 1 5

Journal scopeJournal of Physics A: Mathematical and Theoretical is a major journal of theoretical physics reporting research on the mathematical structures that describe fundamental processes of the physical world and on the analytical, computational and numerical methods for exploring these structures.

Mathematical papers should be clearly motivated by actual or potential application to physical phenomena. Research papers published in Journal of Physics A: Mathematical and Theoretical are categorized into one of six subject sections:

•statistical physics

•chaotic and complex systems

•mathematical physics

•quantum mechanics and quantum information theory

•field theory and string theory

•fluid and plasma theory

To be accepted for publication in the journal, papers must make significant, original and correct contributions to one or more of the topics within these sections.

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ISSN 1751-8113

Journal of Physics A

Volume 44 Number 50 16 December 2011

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Contents

Universal statistics and control of random transport processes 9Iddo Eliazar and Joseph Klafter

Fermi edge resonances in non-equilibrium states of Fermi gases 9E Bettelheim, Y Kaplan and P Wiegmann

Functional Bethe ansatz methods for the open XXX chain 9Holger Frahm, Jan H Grelik, Alexander Seel and Tobias Wirth

An exact formula for the statistics of the current in the TASEP with open boundaries 9Alexandre Lazarescu and Kirone Mallick

The grand canonical ABC model: a reflection asymmetric mean-field Potts model 10J Barton, J L Lebowitz and E R Speer

Non-equilibrium 1D many-body problems and asymptotic properties of Toeplitz determinants 10D B Gutman, Yuval Gefen and A D Mirlin

Residual mean first-passage time for jump processes: theory and applications to Lévy flights and fractional Brownian motion 10V Tejedor, O Bénichou, Ralf Metzler and R Voituriez

Thermodynamics and spin-charge separation of one-dimensional strongly repulsive three-component fermions 11Peng He, Jen Yee Lee, Xiwen Guan, Murray T Batchelor and Yupeng Wang

Diffusion with optimal resetting 11Martin R Evans and Satya N Majumdar

Replica approach to the KPZ equation with the half Brownian motion initial condition 11Takashi Imamura and Tomohiro Sasamoto

Universal emergence of PageRank 12K M Frahm, B Georgeot and D L Shepelyansky

Optimum principle for a vehicular traffic network: minimum probability of congestion 12Boris S Kerner

Loschmidt echo in quantum maps: the elusive nature of the Lyapunov regime 12Ignacio García-Mata and Diego A Wisniacki

Isochronal synchronization of time delay and delay-coupled chaotic systems 13J M V Grzybowski , E E N Macau and T Yoneyama

Time-dependent scattering theory for ODEs and applications to reaction dynamics 13Daniel Blazevski and Rafael de la Llave

Statistical physics

Chaotic and complex systems

Insight available

In

In

In

In


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A compact hamiltonian with the same asymptotic mean spectral density as the Riemann zeros 14M V Berry and J P Keating

On natural Poisson bivectors on the sphere 14A V Tsiganov

A modular invariant bulk theory for the c=0 triplet model 14Matthias R Gaberdiel, Ingo Runkel and Simon Wood

On sums of tensor and fusion multiplicities 14Robert Coquereaux and Jean-Bernard Zuber

Highest weight Macdonald and Jack polynomials 15Th Jolicoeur and J G Luque

Quantum loop subalgebra and eigenvectors of the superintegrable chiral Potts transfer matrices 15Helen Au-Yang and Jacques H H Perk

Solvable vector nonlinear Riemann problems, exact implicit solutions of dispersionless PDEs and wave breaking 15S V Manakov and P M Santini

The classical trigonometric r-matrix for the quantum-deformed Hubbard chain 16Niklas Beisert

A nonseparable quantum superintegrable system in 2D real Euclidean space 16Sarah Post and Pavel Winternitz

The Berry–Keating Hamiltonian and the local Riemann hypothesis 16Mark Srednicki

Non-equilibrium steady states of quantum systems on star graphs 17Mihail Mintchev

The quantum Arnold transformation 17V Aldaya, F Cossío, J Guerrero and F F López-Ruiz

A note on the optimality of decomposable entanglement witnesses and completely entangled subspaces 17R Augusiak, J Tura and M Lewenstein

Complete characterization of extreme quantum observables in infinite dimensions 17Juha-Pekka Pellonpää

Extremal correlations of the tripartite no-signaling polytope 18Stefano Pironio, Jean-Daniel Bancal and Valerio Scarani

Correlation-induced non-Abelian quantum holonomies 18Markus Johansson, Marie Ericsson, Kuldip Singh, Erik Sjöqvist and Mark S Williamson

Physics within a quantum reference frame 18Renato M Angelo, Nicolas Brunner, Sandu Popescu, Anthony J Short and Paul Skrzypczyk

Mathematical physics

Quantum mechanics and quantum information theory

In

In

Insight availableIn


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Constructions and noise threshold of topological subsystem codes 19Martin Suchara, Sergey Bravyi and Barbara Terhal

Simulating quantum dynamics on a quantum computer 19Nathan Wiebe, Dominic W Berry, Peter Høyer and Barry C Sanders

Low-dimensional quite noisy bound entanglement with a cryptographic key 19Łukasz Pankowski and Michał Horodecki

Nonassociative gravity in string theory? 20R Blumenhagen and E Plauschinn

Symmetries of noncommutative scalar field theory 20Axel de Goursac and Jean-Christophe Wallet

Frame-like geometry of double field theory 20Olaf Hohm and Seung Ki Kwak

Amplitudes at weak coupling as polytopes in AdS5 20Lionel Mason and David Skinner

Complete conformal field theory solution of a chiral six-point correlation function 21Jacob J H Simmons and Peter Kleban

Lifshitz formula for the Casimir force and the Gelfand–Yaglom theorem 21C Ccapa Ttira, C D Fosco and F D Mazzitelli

On strong-coupling correlation functions of circular Wilson loops and local operators 21Luis F Alday and Arkady A Tseytlin

W-algebras and surface operators in N=2 gauge theories 21Niclas Wyllard

An action principle for Vasiliev’s four-dimensional higher spin gravity 22Nicolas Boulanger and Per Sundell

N=2 S-duality via outer-automorphism twists 22Yuji Tachikawa

Lyapunov exponent for small particles in smooth one-dimensional flows 22Michael Wilkinson

Landau damping: the mechanics model and its ultimate entropy gain 22J H Hannay and Michel Kluge

Exploring Born–Infeld electrodynamics using plasmas 23D A Burton, R M G M Trines, T J Walton and H Wen

Application of the multicomponent lattice Boltzmann simulation method to oil/water dispersions 23M A Seaton, I Halliday and A J Masters

Differential geometric structures of stream functions: incompressible two-dimensional flow and curvatures 23K Yamasaki, T Yajima and T Iwayama

Field theory and string theory

Fluid and plasma theory

Journal of Physics A invites you to submit your article online atauthors.iop.org

http://authors.iop.org


H i g h l i g h t s o f 2 0 1 1 9

Universal statistics and control of random transport processes

Iddo Eliazar1 and Joseph Klafter2 1 Department of Technology Management, Holon Institute of Technology, PO Box 305, Holon 58102, Israel

2 School of Chemistry, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel

2011 J. Phys. A: Math. Theor. 44 222001

A general model of random transport is considered: independent agents are stochastically emitted into a space with general topology; the agents’ motion in space is governed by a general random transport mechanism; the agents are detected only when in a target zone which is an arbitrary subset of space. We explore emission intensities which render the agents’ ‘target-zone statistics’ universal, i.e. invariant with respect to the underlying spatial topology and transport mechanism. The results established determine how to universally control the target-zone statistics via the emission intensity, and show that the resulting universal statistics are governed by power laws.

Occupation of electronic states in a structured Fermi sea.

Statistical physicsq

Fast Track Communications

Fermi edge resonances in non-equilibrium states of Fermi gases

E Bettelheim1, Y Kaplan1 and P Wiegmann2 1 Racah Institute of Physics, Hebrew University, Jerusalem, Israel2 The James Franck Institute, University of Chicago, Chicago, IL, USA


We formulate the problem of the Fermi edge singularity in non-equilibrium states of a Fermi gas as a matrix Riemann–Hilbert problem with an integrable kernel. This formulation is the most suitable for studying the singular behavior at each edge of non-equilibrium Fermi states by means of the method of steepest descent, and also reveals the integrable structure of the problem. We supplement this result by extending the familiar approach to the problem of the Fermi edge singularity via the bosonic representation of the electronic operators to non-equilibrium settings. It provides a compact way to extract the leading asymptotes.


Functional Bethe ansatz methods for the open XXX chain

Holger Frahm, Jan H Grelik, Alexander Seel and Tobias Wirth

Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstr. 2, 30167 Hannover, Germany


We study the spectrum of the integrable open XXX Heisenberg spin chain subject to non-diagonal boundary magnetic fields. The spectral problem for this model can be formulated in terms of functional equations obtained by separation of variables or, equivalently, from the fusion of transfer matrices. For generic boundary conditions the eigenvalues cannot be obtained from the solution of finitely many algebraic Bethe equations. Based on careful finite size studies of the analytic properties of the underlying hierarchy of transfer matrices we devise two approaches to analyze the functional equations. First we introduce a truncation method leading to Bethe-type equations determining the energy spectrum of the spin chain. In a second approach, the hierarchy of functional equations is mapped to an infinite system of nonlinear integral equations of TBA type. The two schemes have complementary ranges of applicability and facilitate an efficient numerical analysis for a wide range of boundary parameters. Some data are presented on the finite-size corrections to the energy of the state which evolves into the antiferromagnetic ground state in the limit of parallel boundary fields.

Root distributions for the B-state at α ± = 11i/3 and ch φ = 11. Zeros belonging to fixed lattice sizes L = 1–9 are each connected by a dashed line as a guidance for the eyes. The roots on the imaginary axis forming an asymptotic lattice of half-integers are not displayed.

An exact formula for the statistics of the current in the TASEP with open boundaries

Alexandre Lazarescu and Kirone Mallick

Institut de Physique Théorique, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France


We study the totally asymmetric exclusion process on a finite one-dimensional lattice with open boundaries, i.e. in contact with two reservoirs at different potentials. The total (time-integrated) current through the system is a random variable that scales linearly with time in the long-time limit. We conjecture a parametric representation for the generating function of the cumulants of the current, which is related to the large deviation function by Laplace transform. This formula is valid for all system sizes and for all values of the boundary coupling parameters.

Illustration of the TASEP with open boundaries on a finite lattice with L sites.

http://iopscience.iop.org/1751-8121/44/22/222001





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The grand canonical ABC model: a reflection asymmetric mean-field Potts model

J Barton1, J L Lebowitz1,2 and E R Speer2 1 Department of Physics, Rutgers University, Piscataway, NJ 08854-8019, USA2 Department of Mathematics, Rutgers University, Piscataway, NJ 08854-8019, USA


We investigate the phase diagram of a three-component system of particles on a one-dimensional filled lattice, or equivalently of a one-dimensional three-state Potts model, with reflection asymmetric mean-field interactions. The three types of particles are designated as A, B and C. The system is described by a grand canonical ensemble with temperature T and chemical potentials TλA, TλB and TλC. We find that for λA = λB = λC the system undergoes a phase transition from a uniform density to a continuum of phases at a critical temperature T c=(2π /√3)–1. For other values of the chemical potentials the system has a unique equilibrium state. As is the case for the canonical ensemble for this ABC model, the grand canonical ensemble is the stationary measure satisfying detailed balance for a natural dynamics. We note that T c=3Tc, where Tc is the critical temperature for a similar transition in the canonical ensemble at fixed equal densities rA = rB = rC = 1/3.

Curves Γβ in the rA–rB plane along which F(r) achieves its minimum value, for β1 = 3.75, β2 = 4.25 and β3 = 6.05 (βtc = 2π/√3 b 3.63).

Non-equilibrium 1D many-body problems and asymptotic properties of Toeplitz determinants

D B Gutman1, Yuval Gefen2 and A D Mirlin3,4,5 1 Department of Physics, Bar Ilan University, Ramat Gan 52900, Israel2 Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel

3 Institut für Nanotechnologie, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany

4 Institut für Theorie der kondensierten Materie, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany

5 Petersburg Nuclear Physics Institute, 188300 St. Petersburg, Russia


Non-equilibrium bosonization technique facilitates the solution of a number of important many-body problems out of equilibrium, including the Fermi-edge singularity, the tunneling spectroscopy and full counting statistics of interacting fermions forming a Luttinger liquid. We generalize the method to non-equilibrium hard-core bosons (Tonks–Girardeau gas)

and establish interrelations between all these problems. The results can be expressed in terms of Fredholm determinants of the Toeplitz type. We analyze the long time asymptotics of such determinants, using Szego and Fisher–Hartwig theorems. Our analysis yields dephasing rates as well as power-law scaling behavior, with exponents depending not only on the interaction strength but also on the non-equilibrium state of the system.

Schematic results for TDOS in a LL with not-too-strong interaction and with multiple-step distributions. The distributions of electrons from both reservoirs are assumed to be equal and of the type shown in figure 1(A) (upper panel) or figure 1(B) (lower panel). The exponents γi characterizing ZBA at multiple edges are indicated. All singularities are broadened by the non-equilibrium dephasing rate 1/2τφ.

Residual mean first-passage time for jump processes: theory and applications to Lévy flights and fractional Brownian motion

V Tejedor1,2, O Bénichou1, Ralf Metzler2,3 and R Voituriez1

1 Laboratoire de Physique Théorique de la Matière Condensée (UMR 7600), Université Pierre et Marie Curie, 4 Place Jussieu, 75255 Paris Cedex, France

2 Physics Department, Technical University of Munich, James Franck Strasse, 85747 Garching, Germany

3 Physics Department, Tampere University of Technology, FI-33101 Tampere, Finland


We derive a functional equation for the mean first-passage time (MFPT) of a generic self-similar Markovian continuous process to a target in a one-dimensional domain and obtain its exact solution. We show that the obtained expression of the MFPT for continuous processes is actually different from the large system size limit of the MFPT for discrete jump processes allowing leapovers. In the case considered here, the asymptotic MFPT admits non-vanishing corrections, which we call residual MFPT. The case of Lévy flights with diverging variance of jump lengths is investigated in detail, in particular, with respect to the associated leapover behavior. We also show numerically that our results apply with good accuracy to fractional Brownian motion, despite its non-Markovian nature.

MFPT for a Lévy flight, for several sizes of the 1D lattice (200, 400, 800, 1600, 3200 and 6400 sites, from black (bottom) to light gray (top) as the size grows) compared to the theoretical expression (16) (magenta dotted line, the A constant being given by equation (23)), and for dw = 1.25.





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Replica approach to the KPZ equation with the half Brownian motion initial condition

Takashi Imamura1 and Tomohiro Sasamoto2 1 Research Center for Advanced Science and Technology, The University of Tokyo, Japan

2 Department of Mathematics and Informatics, Chiba University, Japan


We consider the one-dimensional Kardar–Parisi–Zhang (KPZ) equation with the half Brownian motion initial condition, studied previously through the weakly asymmetric simple exclusion process. We employ the replica Bethe ansatz and show that the generating function of the exponential moments of the height is expressed as a Fredholm determinant. From this, the height distribution and its asymptotics are studied. Furthermore, using the replica method we also discuss the multi-point height distribution. We find that some good properties of the deformed Airy functions play an important role in the analysis.

Half Brownian motion initial condition.

Thermodynamics and spin-charge separation of one-dimensional strongly repulsive three-component fermions

Peng He1,2, Jen Yee Lee2, Xiwen Guan2, Murray T Batchelor2,3 and Yupeng Wang1 1 Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China

2 Department of Theoretical Physics, Research School of Physics and Engineering, Australian National University, Canberra ACT 0200, Australia

3 Mathematical Sciences Institute, Australian National University, Canberra ACT 0200, Australia


The low-temperature thermodynamics of one-dimensional strongly repulsive SU(3) fermions in the presence of a magnetic field is investigated via the Yang–Yang thermodynamic Bethe ansatz method. The analytical free energy and magnetic properties of the model at low temperatures in a weak magnetic field are derived via the Wiener–Hopf method. It is shown that the low-energy physics can be described by spin-charge separated conformal field theories of an effective Tomonaga–Luttinger liquid and an antiferromagnetic SU(3) Heisenberg spin chain. Beyond the Tomonaga–Luttinger liquid regime, the equation of state is given in terms of the polylog function for a weak external field. The results obtained are essential for further study of quantum criticality in strongly repulsive three-component fermions.

The plot shows CV –T curves for external magnetic field H = 0.001, chemicalpotential µ = 6 and coupling constant c = 30.

Diffusion with optimal resetting

Martin R Evans1,2 and Satya N Majumdar2,3 1 SUPA, School of Physics and Astronomy, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, UK

2 Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel

3 University Paris-Sud, CNRS, LPTMS, UMR 8626, Orsay F-01405, France


We consider the mean time to absorption by an absorbing target of a diffusive particle with the addition of a process whereby the particle is reset to its initial position with rate r. We consider several generalizations of the model of Evans and Majumdar (2011 Phys. Rev. Lett. 106 160601): (i) a space-dependent resetting rate r(x); (ii) resetting to a random position z drawn from a resetting distribution P(z); and (iii) a spatial distribution for the absorbing target PT(x). As an example of (i) we show that the introduction of a non-resetting window around the initial position

can reduce the mean time to absorption provided that the initial position is sufficiently far from the target. We address the problem of optimal resetting, that is, minimizing the mean time to absorption for a given target distribution. For an exponentially decaying target distribution centred at the origin we show that a transition in the optimal resetting distribution occurs as the target distribution narrows.

Schematic spacetime trajectory of a one-dimensional Brownian motion that starts at x

0 and resets stochastically to its initial position x

0 at rate r.

PEER REVIEW TIMES IN 2011First decision times*

*median receipt to first decision time

34 DAYS





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Optimum principle for a vehicular traffic network: minimum probability of congestion

Boris S Kerner

Daimler AG, GR/PTF, HPC: G021, 71059 Sindelfingen, Germany


We introduce an optimum principle for a vehicular traffic network with road bottlenecks. This network breakdown minimization (BM) principle states that the network optimum is reached when link flow rates are assigned in the network in such a way that the probability for spontaneous occurrence of traffic breakdown in at least one of the network bottlenecks during a given observation time reaches the minimum possible value. Based on numerical

Chaotic and complex systemsq


Insightavailable

Probability of traffic breakdown PFS(B)

at a single on-ramp bottleneck as a function of the flow rate downstream of the bottleneck for on-ramp inflow rates q

on = 1000 vehicles h−1.

Universal emergence of PageRank

K M Frahm, B Georgeot and D L Shepelyansky

Laboratoire de Physique Théorique du CNRS, IRSAMC, Université de Toulouse, UPS, 31062 Toulouse, France


The PageRank algorithm enables us to rank the nodes of a network through a specific eigenvector of the Google matrix, using a damping parameter α e ]0, 1[. Using extensive numerical simulations of large web networks, with a special accent on British University networks, we determine numerically and analytically the universal features of the PageRank vector at its emergence when α → 1. The whole network can be divided into a core part and a group of invariant subspaces. For α → 1, PageRank converges to a universal power-law distribution on the invariant subspaces whose size distribution also follows a universal power law. The convergence of PageRank at α → 1 is controlled by eigenvalues of the core part of the Google matrix, which are extremely close to unity, leading to large relaxation times as, for example, in spin glasses.

Insightavailable

Left panels (right panels) correspond to Cambridge 2006 (Oxford 2006). Subspace eigenvalues of the matrix S (blue dots or crosses) and core space eigenvalues (red dots) in the λ–plane (green curve shows unit circle); here Ns = 48 239 (30 579). There are 1543 (1889) invariant subspaces, with maximal dimension 4656 (1545) and the sum of all subspace dimensions is Ns = 48 239 (30 579). The core space eigenvalues are obtained from the AM applied to the block Scc with Arnoldi dimension 20 000 and are numerically accurate for |λ|H 0.7.

Loschmidt echo in quantum maps: the elusive nature of the Lyapunov regime

Ignacio García-Mata1,2,3 and Diego A Wisniacki4

1 Departamento de Física, Lab. TANDAR–CNEA, Buenos Aires, Argentina2 Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), CONICET–UNMdP, Funes 3350, B7602AYL Mar del Plata, Argentina

3 Consejo Nacional de Investigaciones Científicas y Tecnológicas (CONICET), Argentina

4 Departamento de Física, FCEyN UBA, and IFIBA, CONICET, Pabellón 1 Ciudad Universitaria, C1428EGA Buenos Aires, Argentina


The Loschmidt echo (LE) is a measure of the stability and reversibility of quantum evolution under perturbations of the Hamiltonian. One of the expected and most relevant characteristics of this quantity for chaotic systems is an exponential decay with a perturbation-independent decay rate given by the classical Lyapunov exponent. However, a non-uniform decay—instead of the Lyapunov regime—has been reported in several systems. In this work, we find an analytical semiclassical expression for the averaged fidelity amplitude that can be directly related to the anomalous—unexpected—behaviour of the LE.

Decay rate ΓLE as a function of the rescaled perturbation Σ/h– for the quantum perturbed cat map with N = 218 and for different values of a and b (different values of λ, indicated by the dashed lines). (4) a = b = 1, λ ≈ 0.96; (L) a = b = 2, λ ≈ 1.76; (3) a = b = 4, λ ≈ 2.887; (X) a = b = 6, λ ≈ 3.637; (o) a = b = 20, λ ≈ 5.996. The perturbation is f

1(q) (equation (27)). The solid line corresponds to ΓDR

AFA and the dash-dot line σSC LDOS. Averages were done over 2048 initial states.

simulations with a stochastic three-phase traffic flow model, we show that in comparison to the well-known Wardrops principles, the application of the BM principle permits considerably greater network inflow rates at which no traffic breakdown occurs and, therefore, free flow remains in the whole network.





H i g h l i g h t s o f 2 0 1 1 13

Isochronal synchronization of time delay and delay-coupled chaotic systems

J M V Grzybowski1, E E N Macau2 and T Yoneyama3

1 Instituto Tecnológico de Aeronáutica, ITA, Praça Marechal Eduardo Gomes, 50, Vila das Acácias, São José dos Campos, SP, Brazil, CEP 12.228-900

2 Instituto Nacional de Pesquisas Espaciais, INPE, PO Box 515, São José dos Campos, SP, Brazil, CEP 12.227-010

3 Instituto Tecnológico de Aeronáutica, ITA, Praça Marechal Eduardo Gomes, 50, Vila das Acácias, São José dos Campos, SP, Brazil, CEP 12.228-900


This paper studies the problem of isochronal synchronization of time-delay chaotic systems featuring also coupling delay. Based on the Lyapunov–Krasovskii stability theory, sufficient conditions are derived for the stability of isochronal synchronization between a pair of identical chaotic systems. Such criteria permit the proper design of stable proportional linear feedback controller, more specifically, the design of adequate proportional feedback gain matrices. The proposed criteria are suited to systems with (i) intrinsic delay, (ii) coupling delay or (iii) both. Numerical simulations of the synchronization of delay-coupled systems are presented as examples of the application of the criteria.

Insightavailable

Synchronization error for the Lorenz hyperchaotic system, τ = 0.2.

Time-dependent scattering theory for ODEs and applications to reaction dynamics

Daniel Blazevski and Rafael de la Llave

Department of Mathematics, University of Texas, 1 University Station C1200, Austin, TX 78712, USA


We develop a time-dependent scattering theory for general vector fields in Euclidean space. We give conditions that ensure that the wave maps exist, are smooth, invertible, and depend smoothly on parameters. We then discuss the intertwining relations and how they can be used to compute stable/unstable manifolds for time-dependent normally hyperbolic invariant manifolds. The theory is particularly effective for Hamiltonian mechanics. We also give perturbative calculations of the scattering map that are analogous to Fermi's golden rule in quantum mechanics. We apply this theory to a problem in transition state theory concerning the exposure of molecules to a laser pulse for a short time. We present a method to compute invariant manifolds for the laser-driven Henon–Heilies system and give perturbative calculations of the change in the branching ratio.

Pictorial description of the wave and scattering maps. For a given point x

0 let x

0± := X ±

t0. Then Vt0t (x0) converges in the future

(resp. past) to Ut0t (x0

+) (resp. Ut0–t (x0

–)) and the scattering map takes x

0– as an input and

outputs x0+.

Visit our homepage to read what our authors have to say about their work

Insights




14 H i g h l i g h t s o f 2 0 1 1

Mathematical physicsq

A compact hamiltonian with the same asymptotic mean spectral density as the Riemann zeros

M V Berry1 and J P Keating2

1 H H Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, UK2 School of Mathematics, University of Bristol, Bristol BS8 1TW, UK


For the classical hamiltonian (x + 1/x)(p + 1/p), with position x and conjugate momentum p, all orbits are bounded. After a symmetrization, the corresponding quantum integral equation possesses a family of self-adjoint extensions: compact operators on the entire positive x axis, labelled by an angle α specifying the boundary condition at the origin, with a discrete spectrum of real energies E. On the cylinder {−∞ < E < ∞, 0 G α < 2π}, there is a single eigencurve in the form of a helix winding clockwise. The rise between successive windings gets sharper as the scaled Planck's constant decreases. This behaviour can be understood semiclassically. The first two terms of the asymptotic eigenvalue density are the same as those for the density of heights of the Riemann zeros.

(a) 3D plot of hamiltonian H(x, p) (1.3), with quadrants labelled Q. (b) Shaded contourplot of H(x, p) in first quadrant, with light representing high and dark low.

A modular invariant bulk theory for the c=0 triplet model

Matthias R Gaberdiel1, Ingo Runkel2 and Simon Wood1

1 Institute for Theoretical Physics, ETH Zürich, 8093 Zürich, Switzerland2 Department Mathematik, Universität Hamburg, Bundesstraße 55, 20146 Hamburg, Germany


A proposal for the bulk space of the logarithmic W2,3-triplet model at central charge zero is made. The construction is based on the idea that one may reconstruct the bulk theory of a rational conformal field theory from its boundary theory. The resulting bulk space is a quotient of the direct sum of projective representations, which is isomorphic, as a vector space, to the direct sum of tensor products of the irreducible representations with their projective covers. As a consistency check of our analysis, we show that the partition function of the bulk theory is modular invariant, and that the boundary state analysis is compatible with the proposed annulus partition functions of this model.

On sums of tensor and fusion multiplicities

Robert Coquereaux1 and Jean-Bernard Zuber2

1 Centre de Physique Théorique (CPT), CNRS UMR 6207, Luminy, Marseille, France2 Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589 and Université Pierre et Marie Curie-Paris 6, 4 Place Jussieu, 75252 Paris Cedex 05, France


The total multiplicity in the decomposition into irreducibles of the tensor product λ ⊗ μ of two irreducible representations of a simple Lie algebra is invariant under conjugation of one of them: Σν N

λ μν = Σν N-

λ μν. This

also applies to the fusion multiplicities of affine algebras in conformal WZW theories. In that context, the statement is equivalent to a property of the modular S-matrix, namely Σ(κ) := Σ

λSλκ

= 0 if κ is a complex representation. Curiously, this vanishing Σ(κ) also holds when κ is a quaternionic representation. We provide proofs of all these statements. These proofs rely on a case-by-case analysis, maybe overlooking some hidden symmetry principle. We also give various illustrations of these properties in the contexts of boundary conformal field theories, integrable quantum field theories and topological field theories.

The tensor product graph Nf for the subgroup Σ(1080).

On natural Poisson bivectors on the sphere

A V Tsiganov

St. Petersburg State University, St. Petersburg, Russia


We discuss the concept of natural Poisson bivectors, which allows us to consider the overwhelming majority of known integrable systems on the sphere in the framework of bi-Hamiltonian geometry.






H i g h l i g h t s o f 2 0 1 1 15

Highest weight Macdonald and Jack polynomials

Th Jolicoeur1 and J G Luque2

1 LPTMS, CNRS et Université Paris-Sud, 91405 Orsay, France2 Laboratoire LITIS, EA 4108, Université de Rouen, Avenue de l’Université, BP 8 76801 Saint-Étienne-du-Rouvray Cedex, France


Fractional quantum Hall states of particles in the lowest Landau levels are described by multivariate polynomials. The incompressible liquid states when described on a sphere are fully invariant under the rotation group. Excited quasiparticle/quasihole states are members of multiplets under the rotation group and generically there is a nontrivial highest weight member of the multiplet from which all states can be constructed. Some of the trial states proposed in the literature belong to classical families of symmetric polynomials. In this paper we study Macdonald and Jack polynomials that are highest weight states. For Macdonald polynomials, it is a (q, t)-deformation of the raising angular momentum operator that defines the highest weight condition. By specialization of the parameters we obtain a classification of the highest weight Jack polynomials. Our results are valid in the case of staircase and rectangular partition indexing the polynomials.

Quantum loop subalgebra and eigenvectors of the superintegrable chiral Potts transfer matrices

Helen Au-Yang1,2 and Jacques H H Perk1,2

1 Department of Physics, Oklahoma State University, 145 Physical Sciences, Stillwater, OK 74078-3072, USA

2 Centre for Mathematics and its Applications & Department of Theoretical Physics, Australian National University, Canberra, ACT 2600, Australia


It has been shown in earlier works that for Q = 0 and L a multiple of N, the ground state sector eigenspace of the superintegrable τ2(tq) model is highly degenerate and is generated by a quantum loop algebra L(sl

2). Furthermore, this loop algebra can be decomposed into r = (N − 1)L/N simple sl

2 algebras. For Q ≠ 0, we shall show here that the corresponding eigenspace of τ

2(tq) is still highly degenerate, but splits into two spaces, each containing 2r − 1 independent eigenvectors. The generators for the sl

2 subalgebras, and also for the quantum loop subalgebra, are given generalizing those in the Q = 0 case. However, the Serre relations for the generators of the loop subalgebra are only proven for some states, tested on small systems and conjectured otherwise. Assuming their validity we construct the eigenvectors of the Q ≠ 0 ground state sectors for the transfer matrix of the superintegrable chiral Potts model.

Solvable vector nonlinear Riemann problems, exact implicit solutions of dispersionless PDEs and wave breaking

S V Manakov1 and P M Santini2

1 Landau Institute for Theoretical Physics, Moscow, Russia2 Dipartimento di Fisica, Università di Roma ‘La Sapienza’, and Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, Piazz.le Aldo Moro 2, I-00185 Roma, Italy


We have recently solved the inverse spectral problem for integrable partial differential equations (PDEs) in arbitrary dimensions arising as commutation of multidimensional vector fields depending on a spectral parameter λ. The associated inverse problem, in particular, can be formulated as a nonlinear Riemann–Hilbert (NRH) problem on a given contour of the complex λ plane. The most distinguished examples of integrable PDEs of this type, like the dispersionless Kadomtsev–Petviashivili (dKP), the heavenly and the two-dimensional dispersionless Toda equations, are real PDEs associated with Hamiltonian vector fields. The corresponding NRH data satisfy suitable reality and symplectic constraints. In this paper, generalizing the examples of solvable NRH problems illustrated in Manakov and Santini (2009 J. Phys. A: Math. Theor. 42 095203; 2008 J. Phys. A: Math. Theor. 41 055204; 2009 J. Phys. A: Math. Theor. 42 404013), we present a general procedure to construct solvable NRH problems for integrable real PDEs associated with Hamiltonian vector fields, allowing one to construct exact implicit solutions of such PDEs parametrized by an arbitrary number of real functions of a single variable. Then, we illustrate this theory on few distinguished examples for the dKP and heavenly equations. For the dKP case, we characterize a class of similarity solutions, of solutions constant on their parabolic wave front and breaking simultaneously on it, of localized solutions whose breaking point travels with constant speed along the wave front, and of localized solutions breaking in a point of the (x, y) plane. For the heavenly equation, we characterize two classes of symmetry reductions.

The saddle wave front described by (114), before breaking, for n = 4, a = 0.3, F(ζ) = 0.2e− ζ 2 and t = tb − 1, where tb = 25e/8.





16 H i g h l i g h t s o f 2 0 1 1

The Berry–Keating Hamiltonian and the local Riemann hypothesis

Mark Srednicki

Department of Physics, University of California, Santa Barbara, CA 93106, USA


The local Riemann hypothesis states that the zeros of the Mellin transform of a harmonic-oscillator eigenfunction (on a real or p-adic configuration space) have a real part 1/2. For the real case, we show that the imaginary parts of these zeros are the eigenvalues of the Berry–Keating Hamiltonian H

BK = (x p + p x)/2 projected onto the subspace of oscillator eigenfunctions of a lower level. This gives a spectral proof of the local Riemann hypothesis for the reals, in the spirit of the Hilbert–Pólya conjecture. The p-adic case is also discussed.

The classical trigonometric r-matrix for the quantum-deformed Hubbard chain

Niklas Beisert

Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, 14476 Potsdam, Germany


The one-dimensional Hubbard model is an exceptional integrable spin chain which is apparently based on a deformation of the Yangian for the superalgebra gl(2|2). Here we investigate the quantum deformation of the Hubbard model in the classical limit. This leads to a novel classical r-matrix of trigonometric kind. We derive the corresponding one-parameter family of Lie bialgebras as a deformation of the affine gl(2|2) Kac–Moody superalgebra. In particular, we discuss the affine extension as well as discrete symmetries, and we scan for simpler limiting cases, such as the rational r-matrix for the undeformed Hubbard model.

The compactified complex plane for z, x or y, respectively. The points corresponding toz±& = 0, ∞ are marked by &. The self-dual points corresponding to z±

* are marked by *. Thespheres are divided into one, two or four regions which are identified by a twist.

A nonseparable quantum superintegrable system in 2D real Euclidean space

Sarah Post1 and Pavel Winternitz1,2

1 Centre de recherches mathématiques, Université de Montréal, C.P. 6128 succ. Centre-Ville, Montréal (QC) H3C 3J7, Canada

2 Département de mathématiques et de statistique, Université de Montréal, C.P. 6128 succ. Centre-Ville, Montréal (QC) H3C 3J7, Canada


In this paper, we derive a nonseparable quantum superintegrable system in 2D real Euclidean space. The Hamiltonian admits no second-order integrals of motion but does admit an integral of third-order and an integral of fourth-order. We also obtain a classical superintegrable system with the same properties. The quantm system differs from the classical one by corrections proportional to h- 2.


Journal of Physics A: Mathematical and Theoretical 2011 topical reviews

On the uncertainty in the regularized solution Daniel Keren and Ido Nissenboim2011 J. Phys. A: Math. Theor. 44 023001

T-systems and Y-systems in integrable systems Atsuo Kuniba, Tomoki Nakanishi and Junji Suzuki2011 J. Phys. A: Math. Theor. 44 103001

Disordered topological insulators: a non-commutative geometry perspective Emil Prodan 2011 J. Phys. A: Math. Theor. 44 113001

Tutorial on scale and conformal symmetries in diverse dimensions R Jackiw and S-Y Pi 2011 J. Phys. A: Math. Theor. 44 223001

Yangians, S-matrices and AdS/CFT Alessandro Torrielli 2011 J. Phys. A: Math. Theor. 44 263001

Scalar field quantization without divergences in all spacetime dimensions John R Klauder 2011 J. Phys. A: Math. Theor. 44 273001

Notes on Yang–Mills–Higgs monopoles and dyons on RD, and Chern–Simons–Higgs solitons on RD–2: dimensional reduction of Chern–Pontryagin densities D H Tchrakian 2011 J. Phys. A: Math. Theor. 44 343001

Discrete quantum mechanicsSatoru Odake and Ryu Sasaki 2011 J. Phys. A: Math. Theor. 44 353001

Lectures on localization and matrix models in supersymmetric Chern–Simons-matter theoriesMarcos Mariño 2011 J. Phys. A: Math. Theor. 44 463001

Unconventional phase transitions in a constrained single polymer chainL I Klushin and A M Skvortsov 2011 J. Phys. A: Math. Theor. 44 473001

The effective temperatureLeticia F Cugliandolo 2011 J. Phys. A: Math. Theor. 44 483001




http://iopscience.iop.org/1751-8121/44/2/023001/



























iopscience.iop.org/1751-8121/44/48/483001/

iopscience.iop.org/1751-8121/44/48/483001/


H i g h l i g h t s o f 2 0 1 1 17

Quantum mechanics and quantum information theory

q

Non-equilibrium steady states of quantum systems on star graphs

Mihail Mintchev

Istituto Nazionale di Fisica Nucleare and Dipartimento di Fisica, Universitá di Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy


Non-equilibrium steady states of quantum fields on star graphs are explicitly constructed. These states are parametrized by the temperature and the chemical potential, associated with each edge of the graph. Time reversal invariance is spontaneously broken. We study in this general framework the transport properties of the Schrödinger and the Dirac systems on a star graph, modeling a quantum wire junction. The interaction, which drives the system away from equilibrium, is localized in the vertex of the graph. All point-like vertex interactions, giving rise to self-adjoint Hamiltonians possibly involving the minimal coupling to a static electromagnetic field in the ambient space, are considered. In this context, we compute the exact electric steady current and the non-equilibrium charge density. We also investigate the heat transport and derive the Casimir energy density away from equilibrium. The appearance of Friedel-type oscillations of the charge and energy densities along the edges of the graph is established. We focus finally on the noise power and discuss the non-trivial impact of the point-like interactions on the noise.

Contour plots of the noise P11 in the plane (β1, β2 ), (μ1,μ2 ) and (η1, η2 ), respectively.

A note on the optimality of decomposable entanglement witnesses and completely entangled subspaces

R Augusiak1, J Tura2 and M Lewenstein1,3,4

1 ICFO–Institut de Ciències Fotòniques, Parc Mediterrani de la Tecnologia, 08860 Castelldefels, Spain

2 Centre de Formació Interdisciplinària Superior, Universitat Politècnica de Catalunya, Pau Gargallo 5, 08028 Barcelona, Spain

3 ICREA–Institució Catalana de Recerca i Estudis Avançats, Lluis Companys 23, 08010 Barcelona, Spain

4 Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106-4030, USA


Entanglement witnesses (EWs) constitute one of the most important entanglement detectors in quantum systems. Nevertheless, their complete characterization, in particular with respect to the notion of optimality, is still missing, even in the decomposable case. Here we show that for any qubit–qunit decomposable EW (DEW) W, the three statements are equivalent: (i) the set of product vectors obeying 〈e, f|W|e, f 〉 = 0 spans the corresponding Hilbert space, (ii) W is optimal, and (iii) W = QΓ, with Q denoting a positive operator supported on a completely entangled subspace (CES) and Γ standing for the partial transposition. While implications (i) (ii) and (ii) (iii) are known, here we prove that (iii) implies (i). This is a consequence of a more general fact saying that product vectors orthogonal to any CES in C2 ⊗ Cn span after partial conjugation the whole space. On the other hand, already in the case of the C3 ⊗ C3 Hilbert space, there exist DEWs for which (iii) does not imply (i). Consequently, either (i) does not imply (ii) or (ii) does not imply (iii), and the above transparent characterization, obeyed by qubit–qunit DEWs, does not hold in general.

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The quantum Arnold transformation

V Aldaya1, F Cossío1, J Guerrero1,2 and F F López-Ruiz1

1 Instituto de Astrofísica de Andalucía, CSIC, Apartado Postal 3004, 18080 Granada, Spain

2 Departamento de Matemática Aplicada, Universidad de Murcia, Campus de Espinardo, 30100 Murcia, Spain


Using a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations, including systems with friction linear in velocity, can be related to the quantum free-particle dynamical system. This transformation provides a basic (Heisenberg–Weyl) algebra of quantum operators, along with well-defined Hermitian operators which can be chosen as evolution-like observables and complete the entire Schrödinger algebra. It also proves to be very helpful in performing certain computations quickly, to obtain, for example, wavefunctions and closed analytic expressions for time-evolution operators.

Complete characterization of extreme quantum observables in infinite dimensions

Juha-Pekka Pellonpää

Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turku, Finland


We give a complete characterization for extreme quantum observables, i.e. for normalized positive operator valued measures (POVMs) which are extremals in the convex set of all POVMs. The characterization is valid both in discrete and continuous cases, and also in the case of an infinite-dimensional Hilbert space. We show that sharp POVMs are pre-processing clean, i.e. they cannot be irreversibly connected to other POVMs via quantum channels.






18 H i g h l i g h t s o f 2 0 1 1

Extremal correlations of the tripartite no-signaling polytope

Stefano Pironio1, Jean-Daniel Bancal2 and Valerio Scarani3

1 Laboratoire d’Information Quantique, Université Libre de Bruxelles, 1050 Brussels, Belgium

2 Group of Applied Physics, University of Geneva, Switzerland 3 Centre for Quantum Technologies and Department of Physics, National University of Singapore, Singapore 117543


The no-signaling polytope associated with a Bell scenario with three parties, two inputs, and two outputs, is found to have 53 856 extremal points, belonging to 46 inequivalent classes. We provide a classification of these points according to various definitions of multipartite nonlocality and briefly discuss other issues such as the interconversion between extremal points seen as a resource and the relation of the extremal points to Bell-type inequalities.

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Correlation-induced non-Abelian quantum holonomies

Markus Johansson1, Marie Ericsson1, Kuldip Singh2, Erik Sjöqvist1,2 and Mark S Williamson2,3

1 Department of Quantum Chemistry, Uppsala University, Box 518, Se-751 20 Uppsala, Sweden

2 Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore

3 Erwin Schrödinger International Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Wien, Austria


In the context of two-particle interferometry, we construct a parallel transport condition that is based on the maximization of coincidence intensity with respect to local unitary operations on one of the subsystems. The dependence on correlation is investigated and it is found that the holonomy group is generally non-Abelian, but Abelian for uncorrelated systems. It is found that our framework contains the Lévay geometric phase (2004 J. Phys. A: Math. Gen. 37 1821) in the case of two-qubit systems undergoing local SU(2) evolutions.

Iterative procedure in the first, second and (n + 1)st step.

Physics within a quantum reference frame

Renato M Angelo1,2, Nicolas Brunner2, Sandu Popescu2, Anthony J Short3 and Paul Skrzypczyk2

1 Federal University of Parana, PO Box 19044, 81531-990, Curitiba, PR, Brazil 2 H H Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, UK

3 DAMTP, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WA, UK


We investigate the physics of quantum reference frames. Specifically, we study several simple scenarios involving a small number of quantum particles, whereby we promote one of these particles to the role of a quantum observer and ask what is the description of the rest of the system, as seen by this observer? We highlight the interesting aspects of such questions by presenting a number of apparent paradoxes. By unravelling these paradoxes, we obtain a better understanding of the physics of quantum reference frames.

At T = 0, a quantum rocket is prepared in a well-localized state, whose centre of mass is depicted here by the narrow central (red) wavepacket. Inside the rocket is a particle in superposition, depicted here by the two outlying (blue) wavepackets, initially located at a distance L from the centre of the rocket, with momentum p towards the centre. At a time T = mpL/p when the wavepackets interfere, either (a) the centre of mass is sufficiently localized to resolve the fringes or (b) the centre of mass is too uncertain to resolve them.

Scan this code with your smartphone to go directly to the online collection.

The selected research highlights are free to read until 31 December 2012.





H i g h l i g h t s o f 2 0 1 1 19

Constructions and noise threshold of topological subsystem codes

Martin Suchara1, Sergey Bravyi2 and Barbara Terhal2

1 Princeton University, Princeton, NJ 08544, USA 2 IBM Watson Research Center, Yorktown Heights, NY 10598, USA


Topological subsystem codes proposed recently by Bombin are quantum error-correcting codes defined on a two-dimensional grid of qubits that permit reliable quantum information storage with a constant error threshold. These codes require only the measurement of two-qubit nearest-neighbor operators for error correction. In this paper, we demonstrate that topological subsystem codes (TSCs) can be viewed as generalizations of Kitaev’s honeycomb model to 3-valent hypergraphs. This new connection provides a systematic way of constructing TSCs and analyzing their properties. We also derive a necessary and sufficient condition under which a syndrome measurement in a subsystem code can be reduced to measurements of the gauge group generators. Furthermore, we propose and implement some candidate decoding algorithms for one particular TSC assuming perfect error correction. Our Monte Carlo simulations indicate that this code, which we call the five-square code, has a threshold against depolarizing noise of at least 2%.

Basis cycles X1, X2 ∈ Z(Lso) corresponding to homologically non-trivial horizontal loops on the lattice.

Simulating quantum dynamics on a quantum computer

Nathan Wiebe1, Dominic W Berry2, Peter Høyer1,3 and Barry C Sanders1,4

1 Institute for Quantum Information Science, University of Calgary, Alberta T2N 1N4, Canada

2 Institute for Quantum Computing, University of Waterloo, Ontario N2 L 3G1, Canada 3 Department of Computer Science, University of Calgary, Alberta T2N 1N4, Canada 4 Department of Physics and Astronomy, University of Calgary, Alberta T2N 1N4, Canada


We explicitly show how to simulate time-dependent sparse Hamiltonian evolution on a quantum computer, with complexity that is close to linear in the evolution time. The complexity also depends on the magnitude of the derivatives of the Hamiltonian. We propose a range of techniques to simulate Hamiltonians with badly behaved derivatives. These include using adaptive time steps, adapting the order of the integrators, and omitting regions about discontinuities. The complexity of the algorithm is quantified by calls to an oracle, which yields information about the Hamiltonian,

and accounts for all computational resources. We explicitly determine the number of bits of output that this oracle needs to provide, and show how to efficiently perform the required 1-sparse unitary operations using these bits. We also account for discretization error in the time, as well as accounting for Hamiltonians that are a sum of terms that are sparse in different bases.

This circuit simulates exp(−iHµ, j (tp)δtp) for the one-sparse Hamiltonian Hµ, j, given an input state of the form of the left-hand side of (66). Here the variable φ = Arg([Hµ, j(tp )]mx,Mx ) and α = 2|[Hµ, j (tp)]mx,Mx|Δtp. Here we also use rectangles to represent Rz rotations by a fixed angle, triangles represent Rx rotations and the pentagon represents a Ry rotation. These rotations can be enacted by querying the oracle QMatrixVal and performing controlled rotations on the output.

Low-dimensional quite noisy bound entanglement with a cryptographic key

Łukasz Pankowski1,2 and Michał Horodecki2

1 Institute of Informatics, University of Gdansk, Gdansk, Poland 2 Institute of Theoretical Physics and Astrophysics, University of Gdansk, Gdansk, Poland


We provide a class of bound entangled states that have a positive distillable secure key rate. The smallest state of this kind is 4 ⊗ 4. Our class is a generalization of the class presented in Horodecki et al (2008 IEEE Trans. Inf. Theory 54 2621–5). It is much wider, containing, in particular, states from the boundary of PPT entangled states (all of the states in the previous class were of this kind) and also states inside the set of PPT entangled states, even approaching the separable states. This generalization comes at a price: for the wider class, a positive key rate requires, in general, apart from the one-way Devetak–Winter protocol (used in the previous case) also the recurrence preprocessing and thus is effectively a two-way protocol. We also analyze the amount of noise that can be admixtured to the states of our class without losing the key distillability property which may be crucial for experimental realization. The wider class contains key-distillable states with higher entropy (up to 3.524, as opposed to 2.564 for the previous class).

A class of key-distillable PPT entangled states: (a) the solid line from u on the boundary of the PPT entangled states (inclusive) to the boundary of the set of separable states, arbitrary close to u

sep; (b) the arc of PPT-invariant states starting in u and approaching arbitrary close to u

max.





20 H i g h l i g h t s o f 2 0 1 1

Field theory and string theoryq

Nonassociative gravity in string theory?

R Blumenhagen1,3 and E Plauschinn2,3

1 Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Föhringer Ring 6, 80805 München, Germany

2 Institute for Theoretical Physics and Spinoza Institute, Utrecht University, 3508 TD Utrecht, The Netherlands

3 Kavli Institute for Theoretical Physics, Kohn Hall, UCSB, Santa Barbara, CA 93106, USA


In an on-shell conformal field theory approach, we find indications of a three-bracket structure for target space coordinates in general closed string backgrounds. This generalizes the appearance of noncommutative gauge theories for open strings in two-form backgrounds to a putative noncommutative/nonassociative gravity theory for closed strings probing curved backgrounds with non-vanishing three-form flux. Several aspects and consequences of the three-bracket structure are discussed and a new type of generalized uncertainty principle is proposed.

Behavior of the three-point function (47) for f123 = √2, k = 1, z3 = 0.

Symmetries of noncommutative scalar field theory

Axel de Goursac1 and Jean-Christophe Wallet2

1 Département de Mathématiques et Physique, Université Catholique de Louvain, Chemin du Cyclotron, 2, 1348 Louvain-la Neuve, Belgium

2 Laboratoire de Physique Théorique, Bât. 210, Université Paris XI, F-91405 Orsay Cedex, France


We investigate symmetries of the scalar field theory with a harmonic term on the Moyal space with the Euclidean scalar product and general symplectic form. The classical action is invariant under the orthogonal group if this group acts also on the symplectic structure. We find that the invariance under the orthogonal group can also be restored at the quantum level by restricting the symplectic structures to a particular orbit.

Frame-like geometry of double field theory

Olaf Hohm and Seung Ki Kwak

Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA


We relate two formulations of the recently constructed double field theory to a frame-like geometrical formalism developed by Siegel. A self-contained presentation of this formalism is given, including a discussion of the constraints and its solutions, and of the resulting Riemann tensor, Ricci tensor and curvature scalar. This curvature scalar can be used to define an action, and it is shown that this action is equivalent to that of double field theory.

Amplitudes at weak coupling as polytopes in AdS5

Lionel Mason1 and David Skinner2

1 The Mathematical Institute, 24–29 St. Giles’, Oxford, OX1 3LB, UK 2 Perimeter Institute for Theoretical Physics, 31 Caroline St, Waterloo, ON, N2L 2Y5, Canada


We show that one-loop scalar box functions can be interpreted as volumes of geodesic tetrahedra embedded in a copy of AdS5 that has dual conformal spacetime as boundary. When the tetrahedron is space-like, it lies in a totally geodesic hyperbolic three-space inside AdS

5, with its four vertices on the boundary. It is a classical result that the volume of such a tetrahedron is given by the Bloch–Wigner dilogarithm. We show that this agrees with the standard physics formulae for such box functions. The combinations of box functions that arise in the n-particle one-loop MHV amplitude in N=4 super Yang–Mills correspond to the volume of a three-dimensional polytope without boundary, all of whose vertices are attached to a null polygon (which in other formulations is interpreted as a Wilson loop) at infinity.

The 3-mass box integral has an entire edge along the boundary at infinity, so its volume diverges. This edge lies along a null geodesic (shown in blue) and the quadric X · X = 0 is ruled by these null lines.

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H i g h l i g h t s o f 2 0 1 1 21

W-algebras and surface operators in N=2 gauge theories

Niclas Wyllard


A general class of W-algebras can be constructed from the affine sl(N) algebra by (quantum) Drinfeld–Sokolov reduction and are classified by partitions of N. Surface operators in an N=2 SU(N) 4D gauge theory are also classified by partitions of N. We argue that instanton partition functions of N=2 gauge theories in the presence of a surface operator can also be computed from the corresponding W-algebra. We test this proposal by analysing the Polyakov–Bershadsky W

3(2) algebra obtaining results

that are in agreement with the known partition functions for SU(3) gauge theories with a so-called simple surface operator. As a byproduct, our proposal implies relations between W

3(2) and W3 algebras.

Complete conformal field theory solution of a chiral six-point correlation function

Jacob J H Simmons1,2 and Peter Kleban3

1 Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP, UK 2 James Franck Institute, 929 E 57th Street, Chicago, IL 60637, USA 3 LASST and Department of Physics & Astronomy, University of Maine, Orono, ME 04469, USA


Using conformal field theory, we perform a complete analysis of the chiral six-point correlation function C(z)=〈φ1,2φ1,2Φ1/2,0(z,z)φ1,2φ1,2〉, with the four φ1,2 operators at the corners of an arbitrary rectangle, and the point z = x + iy in the interior. We calculate this for arbitrary central charge (equivalently, SLE parameter κ > 0). C is of physical interest because for percolation (κ = 6) and many other two-dimensional critical points, it specifies the density at z of critical clusters conditioned to touch either or both vertical ends of the rectangle, with these ends ‘wired’, i.e. constrained to be in a single cluster, and the horizontal ends free. The correlation function may be written as the product of an algebraic prefactor f and a conformal block G, where f = f(x, y, m), with m a cross-ratio specified by the corners (m determines the aspect ratio of the rectangle). By appropriate choice of f and using coordinates that respect the symmetry of the problem, the conformal block G is found to be independent of either y or x, and given by an Appell function.

On strong-coupling correlation functions of circular Wilson loops and local operators

Luis F Alday1 and Arkady A Tseytlin2,3,4

1 Mathematical Institute, University of Oxford, Oxford OX1 3LB, UK 2 Blackett Laboratory, Imperial College, London SW7 2AZ, UK 3 Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA

4 Also at Lebedev Institute, Moscow


Motivated by the problem of understanding 3-point correlation functions of gauge-invariant operators in N=4 super Yang–Mills theory we consider correlators involving Wilson loops and a ‘light’ operator with fixed quantum numbers. At leading order in the strong-coupling expansion such correlators are given by the ‘light’ vertex operator evaluated on a semiclassical string world surface ending on the corresponding loops at the boundary of AdS

5 × S5. We study in detail the example of a correlator of two concentric circular Wilson loops and a dilaton vertex operator. The resulting expression is given by an integral of combinations of elliptic functions and can be computed analytically in some special limits. We also consider a generalization of the minimal surface ending on two circles to the case of non-zero angular momentum J in S5 and discuss a special limit when one of the Wilson loops is effectively replaced by a ‘heavy’ operator with charge J.

The two different solutions approach each other as the corresponding two values of p get closer to p

0.

Lifshitz formula for the Casimir force and the Gelfand–Yaglom theorem

C Ccapa Ttira1, C D Fosco2,3 and F D Mazzitelli3,4

1 Instituto de Fisica – UFRJ, CP 68528, 21941-972 Rio de Janeiro, RJ, Brazil 2 Instituto Balseiro, Universidad Nacional de Cuyo, R8402AGP Bariloche, Argentina 3 Centro Atómico Bariloche, Comisión Nacional de Energía Atómica, R8402AGP Bariloche, Argentina

4 Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón 1, 1428 Buenos Aires, Argentina


We provide a quantum field theory derivation of the Lifshitz formula for the Casimir force due to a fluctuating real scalar field in d + 1 dimensions. The field is coupled to two imperfect, thick, plane mirrors, which are modeled by background potentials localized on their positions. The derivation proceeds from the calculation of the vacuum energy in the Euclidean version of the system, reducing the problem to the evaluation of a functional determinant. The latter is written, via Gelfand–Yaglom's formula, in terms of functions depending on the structure of the potential describing each mirror; those functions encode the properties which are relevant to the Casimir force and are the reflection coefficients evaluated at imaginary frequencies.

The potential V(xd), using a typical profile for the mirrors.






22 H i g h l i g h t s o f 2 0 1 1

An action principle for Vasiliev’s four-dimensional higher spin gravity

Nicolas Boulanger1 and Per Sundell2

Service de Mécanique et Gravitation, Université de Mons—UMONS, 20 Place du Parc, B-7000 Mons, Belgium1 F.R.S.-FNRS Associate Researcher 2 F.R.S.-FNRS Researcher with an Ulysse Incentive Grant for Mobility in Scientific Research


We provide Vasiliev’s fully nonlinear equations of motion for bosonic higher spin gauge fields in four spacetime dimensions with an action principle. We first extend Vasiliev’s original system with differential forms in degrees higher than 1. We then derive the resulting duality-extended equations of motion from a variational principle based on a generalized Hamiltonian sigma-model action. The generalized Hamiltonian contains two types of interaction freedoms: one, a set of functions that appears in the Q-structure of the generalized curvatures of the odd forms in the duality-extended system; and the other, a set depending on the Lagrange multipliers, encoding a generalized Poisson structure, i.e. a set of polyvector fields of rank 2 or higher in target space. We find that at least one of the two sets of interaction-freedom functions must be linear in order to ensure gauge invariance. We discuss consistent truncations to the minimal type A and B models (with only even spins), spectral flows on-shell and provide boundary conditions on fields and gauge parameters that are compatible with the variational principle and that make the duality-extended system equivalent, on-shell, to Vasiliev’s original system.

N=2 S-duality via outer-automorphism twists

Yuji Tachikawa

School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540, USA


Compactification of 6D N=(2,0) theory of type G on a punctured Riemann surface has been effectively used to understand S-dualities of 4D N=2 theories. We can further introduce branch cuts on the Riemann surface across which the worldvolume fields are transformed by the discrete symmetries associated with those of the Dynkin diagram of type G. This allows us to generate more S-dualities, and in particular to reproduce a couple of S-dual pairs found previously by Argyres and Wittig.


(a) This effectively represents a hyper in the bifundamental representation of SO(2N − 1) × USp(2N − 1). (b) Combining with (a) of figure 2, we get superconformal SO(2N − 1) theory.

Fluid and plasma theoryq

Lyapunov exponent for small particles in smooth one-dimensional flows

Michael Wilkinson

Department of Mathematics and Statistics, The Open University, Milton Keynes MK7 6AA, UK


This paper discusses the Lyapunov exponent λ for small particles in a spatially and temporally smooth flow in one dimension. The Lyapunov exponent is obtained as a series expansion in the Stokes number, St, which is a dimensionless measure of the importance of inertial effects. The approach described here can be extended to calculations of the Lyapunov exponents and of the correlation dimension for inertial particles in higher dimensions. It is shown that there is a correction to this theory which arises because the particles do not sample the velocity field ergodically. Using this non-ergodic correction, it is found that (contrary to expectations) the first-order term in the expansion of λ does not vanish.

Landau damping: the mechanics model and its ultimate entropy gain

J H Hannay and Michel Kluge

H.H.Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK


Classical mechanics has only been invoked to account for Landau damping in a rather half-hearted way, alongside plasma perturbation theory. In particular this invocation is essential for the study of the saturation, or post-linear (or ‘nonlinear’) regime of the damping initiated by Dawson and O’Neill. By embracing mechanics wholeheartedly here, with its attendant phase space, one can access results, old and new, cleanly and directly, and with one fewer numerical integration for the post-linear regime. By using a summation technique familiar in semiclassical quantum mechanics (Poisson summation), the one remaining numerical integration can be much improved in accuracy. Also accessible from mechanics is the ultimate entropy gain. Though zero for any finite time (in the absence of coarse graining), the entropy gain is ultimately non-zero (at infinite time the required coarse graining is zero). It is calculated analytically by using the appropriate asymptotics, hitherto not fully exploited.

In Landau damping a particle moves in a sinusoidal potential well, so the phase space energy contours are those of a pendulum with a lemon shaped ‘seperatrix’. The inside of this represents trapping (oscillatory motion), and the outside represents one-way motion (rightwards above, and leftwards below). The initial probability distribution is also shown by shading. It has straight contours, being a (Gaussian) function of velocity only. On the scale of the seperatrix the local behaviour of the probability density is linear.






H i g h l i g h t s o f 2 0 1 1 23

Exploring Born–Infeld electrodynamics using plasmas

D A Burton1,2, R M G M Trines1,3, T J Walton1,2 and H Wen1,2

1 Department of Physics, Lancaster University, Lancaster, UK 2 Cockcroft Institute, Daresbury, UK 3 Rutherford Appleton Laboratory, Chilton, Didcot, UK


The behaviour of large amplitude electrostatic waves in cold plasma is investigated in the context of Born–Infeld electrodynamics. Equations of motion for a relativistic electron fluid in a fixed ion background are established using an unconstrained action principle. A simple expression for the maximum electric field of ‘quasi-static’ electric waves in a cold Born–Infeld plasma is deduced and its properties are analysed. A lower bound on their wavelength is established and an approximation to their frequency is determined for ultrarelativistic phase velocities.

The dashed curve shows μ versus ζ and the solid curve shows E versus ζ (not to scale). Points of intersection of E with the ζ-axis are labelled I and III, and II is a turning point of E. Using (46) and q < 0 it follows dμ/dζ and E are of the opposite sign.

Application of the multicomponent lattice Boltzmann simulation method to oil/water dispersions

M A Seaton1,3, I Halliday2 and A J Masters1

1 School of Chemical Engineering and Analytical Science, The University of Manchester, Oxford Road, Manchester M13 9PL, UK

2 Materials and Engineering Research Institute, Sheffield Hallam University, Howard Street, Sheffield S1 1WB, UK

3 Present address: Computational Science and Engineering Department, STFC Daresbury Laboratory, Keckwick Lane, Daresbury, Warrington, Cheshire WA4 4AD, UK


We study the propagation of acoustic fields in bounded, two-dimensional, mono-disperse oil/water emulsions using a carefully modified and appropriately calibrated single relaxation time multicomponent lattice Boltzmann equation simulation. Our model is a variant of an algorithm applying both interface forces based on macroscopic surface tensions and a kinematic condition for phase separation, adapted to allow sonic speed variations between its oil and water components. Appropriate second-order

accurate acoustic boundary conditions are obtained from a node-based lattice closure with local mass conservation and applicability for varying fluid viscosities. Data from an example simulation of a single oil drop in water interacting with a generated standing acoustic wave are presented and, where appropriate, compared with empirical theories and analogous calculations for a solid object.

Density maps from LB simulation of a standing acoustic wave in water over a period (T = 2π/ωs ≈ 265.8 time steps) with an oil drop, starting at time step 7150.

Differential geometric structures of stream functions: incompressible two-dimensional flow and curvatures

K Yamasaki1, T Yajima2 and T Iwayama1

1 Department of Earth and Planetary Sciences, Faculty of Science, Kobe University, Nada ku, Kobe 657-8501, Japan

2 Department of Physics, Faculty of Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo, 162-8601, Japan


The Okubo–Weiss field, frequently used for partitioning incompressible two-dimensional (2D) fluids into coherent and incoherent regions, corresponds to the Gaussian curvature of the stream function. Therefore, we consider the differential geometric structures of stream functions and calculate the Gaussian curvatures of some basic flows. We find the following. (I) The vorticity corresponds to the mean curvature of the stream function. Thus, the stream-function surface for an irrotational flow and that for a parallel shear flow correspond to the minimal surface and a developable surface, respectively. (II) The relationship between the coherency and the magnitude of the vorticity is interpreted by the curvatures. (III) Using the Gaussian curvature, stability of single and double point vortex streets is analyzed. The results of this analysis are compared with the well-known linear stability analysis. (IV) Conformal mapping in fluid mechanics is the physical expression of the geometric fact that the sign of the Gaussian curvature does not change in conformal mapping. These findings suggest that the curvatures of stream functions are useful for understanding the geometric structure of an incompressible 2D flow.

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Best Paper PrizeSince 2009, Journal of Physics A has awarded a Best Paper Prize, which serves to celebrate well written original research papers that make significant contributions to their fields.

The Editorial Board awarded the 2011 Best Paper Prize to the following papers, which were considered to excel in the criteria of novelty, achievement, potential impact and presentation.

Critical exponents of domain walls in the two-dimensional Potts modelJérôme Dubail, Jesper Lykke Jacobsen and Hubert Saleur2010 J. Phys. A: Math. Theor. 43 482002

An infinite family of solvable and integrable quantum systems on a planeFrédérick Tremblay, Alexander V Turbiner and Pavel Winternitz2009 J. Phys. A: Math. Theor. 42 242001

Thermodynamic Bethe ansatz for planar AdS/CFT: a proposalDiego Bombardelli, Davide Fioravanti and Roberto Tateo2009 J. Phys. A: Math. Theor. 42 375401

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H i g h l i g h t s o f 2 0 1 1 25

2011 special issuesQuantum integrable models and gauge-string duality Guest Editors: P Dorey, J Minahan and A Tseytlin 2011 J. Phys. A: Math. Theor. 44 issue 12 Remarkable progress has been achieved in the last 10 years in the quantitative understanding of gauge/string duality. The most studied example is the most symmetric example of a gauge-string duality—the correspondence between the maximally supersymmetric gauge theory in flat 4 dimensions and superstring theory in a curved space AdS5×S5, also referred to as AdS/CFT duality. The solvability of this model, allowing us for example to compute the dimensions of gauge invariant operators for any value of the coupling, is due to its hidden integrability. The present special issue contains three long reviews that cover recent developments and also present a few particular directions in a detailed pedagogical manner.

This issue features the following papers

Scattering amplitudes in gauge theories: progress and outlookGuest Editors: Radu Roiban, Marcus Spradlin and Anastasia Volovich 2011 J. Phys. A: Math. Theor. 44 issue 45 This issue aims to serve as an introduction to our current understanding of the structure of scattering amplitudes in gauge theory, an area which has seen particularly rapid advances in recent years following decades of steady progress. The articles contained herein provide a snapshot of the latest developments which we hope will serve as a valuable resource for graduate students and other scientists wishing to learn about the current state of the field.

Scattering amplitudes: the most perfect microscopic structures in the universe Lance J Dixon

Tree-level formalism Andreas Brandhuber, Bill Spence and Gabriele Travaglini

Basics of generalized unitarity Zvi Bern and Yu-tin Huang

Generic multiloop methods and application to N = 4 super-Yang–Mills John Joseph M Carrasco and Henrik Johansson

Susy theories and QCD: numerical approachesHarald Ita

Loop amplitudes in gauge theories: modern analytic approaches Ruth Britto

One-loop N = 4 super-Yang–Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loopsR M Schabinger

Scattering amplitudes and Wilson loops in twistor spaceTim Adamo, Mathew Bullimore, Lionel Mason and David Skinner

SUSY Ward identities, superamplitudes and counterterms Henriette Elvang, Daniel Z Freedman and Michael Kiermaier

Tree-level amplitudes and dual superconformal symmetry J M Drummond

Dual conformal symmetry at loop level: massive regularization Johannes M Henn

Exact superconformal and Yangian symmetry of scattering amplitudesTill Bargheer, Niklas Beisert and Florian Loebbert

Integrable spin chains and scattering amplitudes J Bartels, L N Lipatov and A Prygarin

Integrability and the AdS/CFT correspondence Didina Serban

The method of finite-gap integration in classical and semi-classical string theory Benoît Vicedo

Quantum integrability and functional equations: applications to the spectral problem of AdS/CFT and two-dimensional sigma models Dmytro Volin

Featuring the following papers

http://m.iopscience.iop.org/1751-8121/44/12/120301

















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26 H i g h l i g h t s o f 2 0 1 1

Forthcoming special issues for 2012


Coherent states: mathematical and physical aspects

Guest Editors: S Twareque Ali, Jean-Pierre Antoine, Fabio Bagarello and Jean-Pierre Gazeau

Applications of zeta functions and other spectral functions in mathematics and physics: a special issue in honour of Stuart Dowker’s 75th birthday

Guest Editors: Fay Dowker, Emilio Elizalde and Klaus Kirsten

Quantum physics with non-Hermitian operators

Guest Editors: Carl Bender, Andreas Fring, Uwe Guenther and Hugh Jones

Lattice models and integrability: a special issue in honour of F Y Wu

Guest Editors: Anthony Guttmann and Jesper Lykke Jacobsen


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