relativistic bcs-bec crossover in a boson-fermion model qun wang university of science and...
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Relativistic Relativistic BCSBCS--BEC BEC Crossover in a Crossover in a boson-fermion Modelboson-fermion Model
Qun WangUniversity of Science and Technology of China
Motivation Boson-fermion Model Results and discussion Summary and outlook
• Deng, Schmitt, QW, Phys.Rev.D76:034013,2007• Deng, Wang, QW, arXiv:0803.4360
10th workshop for particle physics, Nanjing, April 2008
CCoolloorr superconductivity superconductivity in neutron starsin neutron stars
SStrongly Coupled trongly Coupled QQuark uark GGluon luon PPlasmalasmaIn In RRelativistic elativistic HHeavy eavy IIon on CCollisionsollisions
BCSBCS--BECBEC Crossover Crossover
Science
BCSBCS--BECBEC Crossover Crossover
RRelativistic BCS-BEC crossoverelativistic BCS-BEC crossover
Recent works by other group:
• Nishida & Abuki, PRD 2007 -- NJL approach • Abuki, NPA 2007 – Static and Dynamic properties • Sun, He & Zhuang, PRD 2007 – NJL approach • He & Zhuang, PRD 2007 – Beyond mean field• Kitazawa, Rischke & Shovkovy, arXiv:0709.2235v1 –
NJL+phase diagram• Brauner, arXiv:0803.2422 – Collective excitations
Boson-fermion model (Boson-fermion model (MFAMFA))
With With bosonicbosonic and and fermionicfermionic degrees of freedom with degrees of freedom with
MMean ean FField ield AApproximationpproximation. .
Non-relativistic version: Friedberg, Lee, PRB 1989Friedberg, Lee, Ren, PRB 1990
Thermodynamic potetialThermodynamic potetial
Density and gap Density and gap equationsequations
Crossover parameterCrossover parameter
At zero T or critical TAt zero T or critical T
Dispersion Dispersion relationrelation
In In BCSBCS regime, fermions are slightly gapped, anti- regime, fermions are slightly gapped, anti-fermions are strongly gapped. fermions are strongly gapped.
In In BECBEC regime, both are strongly gapped, indicating the regime, both are strongly gapped, indicating the formation of bound states with large binding energyformation of bound states with large binding energy
Finite TFinite T
BCSBCS regime: regime: Melting condensation Melting condensation of of fermion pairsfermion pairs
BECBEC regime: regime: Melting condensation of Melting condensation of bosonsbosons
Pairing with imbalance populationPairing with imbalance population
• Alford, Berges & Rajagopal, PRL 2000; Alford, Kouvaris & Rajagopal, PRL 04, PRD 05 -- Gapless and crystalline color superconductivity• Huang, Shovkovy, PLB 2003 and NPA 2003; PRD 04; PRD 04 -- Gapless color superconductivity in 2SC, instablility in Meissner masses • Many others ……
Fermi surface topologiesFermi surface topologies
Homogeneous Homogeneous solutionsolution
We use the We use the number susceptibilitynumber susceptibility to tell to tell
which solution are which solution are stablestable..
Phase diagramPhase diagram
The fluctuation of condensateThe fluctuation of condensateCJTCJT formalism formalism
Cornwall, Jackiw, Tomboulis, PRD 1974
2PI diagrams and DS equations2PI diagrams and DS equations
Pseudo-gap (1)Pseudo-gap (1)
Pseudo-gap (2)Pseudo-gap (2)
Gap & Density Gap & Density equationsequations
At small TAt small T
The results are similar to the The results are similar to the MFAMFA results results
At T=TcAt T=Tc
Fluctuations become important in Fluctuations become important in BECBEC regime.regime.In In BECBEC regime T*>Tc. regime T*>Tc.
With increasing TWith increasing T
The fluctuation effects become larger.The fluctuation effects become larger.BEC criterion is related to the minimization BEC criterion is related to the minimization of the thermodynamics potential.of the thermodynamics potential.
SummarySummary
Describe Describe BCSBCS--BECBEC crossover within or beyond crossover within or beyond MFAMFA..
Crossover parameters Crossover parameters xx and and mb2mb2 are equivalent. are equivalent.
Due to relativistic feature, Due to relativistic feature, antiparticleantiparticle must be present. must be present.
With With chemical potential mismatchchemical potential mismatch, some homogeneous , some homogeneous solution are unstable, LOFF or heterogeneous phases should solution are unstable, LOFF or heterogeneous phases should be considered. be considered.
FluctuationFluctuation affects the crossover properties in high affects the crossover properties in high temperature and strong coupling.temperature and strong coupling.
BEC criterionBEC criterion is related to the minimization of the is related to the minimization of the thermodynamics potential.thermodynamics potential.
OutlookOutlook
Our model can be extended to discuss Our model can be extended to discuss quarkoynic quarkoynic continuity with finite chemical continuity with finite chemical potential where the confinement and chiral potential where the confinement and chiral symmetry breaking are not coincide (L. symmetry breaking are not coincide (L. Mclerran and R. D. Pisarski ).Mclerran and R. D. Pisarski ).
BEC criterionBEC criterion for interacting bosons need for interacting bosons need more close look.more close look.
Full self-consistencyFull self-consistency is needed. is needed.
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