MB31 - TRENTOF. Pederiva

D. Lonardoni (Ph.D. Student)A. Roggero (Ph.D. Student)

E. Lipparini (senior) L. Colletti (high school teacher)

(A. Yu Illarionov)

Activities

Nuclear structure: hypernuclei and hyperon physics (talk D. Lonardoni). Neutron stars

Accurate response functions for many-body systems from Integral Transforms (talk A. Roggero)

Low-dimensional electron systems: spin-orbit (Rashba) interactions, inhomogeneous systems.

SNM & PNM @ T > 0

The variational calculations are based on the Gibbs-Bogoliubov inequality:

where ρv is the thermal density matrix defined by:

In FHNC calculations Hv is chosen in such a way that:

where the Ψi are correlated basis states, function of the occupation numbers n(k), and the function εV introduces the temperature dependence$

~0

-60

-50

-40

-30

-20

-10

0

!F

(",T

,1/2

)/A

[M

eV]

T=1 MeVT=5 MeVT=10 MeVT=15 MeVT=20 MeVT=25 MeVT=30 MeV

0 0.08 0.16 0.24 0.32 0.4 0.48 0.56

" [fm-3

]

-60

-50

-40

-30

-20

-10

!F

(",T

,0)/

A [

MeV

]

SNM

PNM

-60

-40

-20

0

20

40

F(!

,T,1

/2)/

A [

MeV

]

AFDMCT=0 MeVT=5 MeVT=10 MeVT=15 MeVT=20 MeVT=25 MeVT=30 MeV

0 0.08 0.16 0.24 0.32 0.4 0.48 0.56

! [fm-3

]

-60

-40

-20

0

20

40

60

80

F(!

,T,0

)/A

[M

eV]

SNM

PNM

We propose a MIXED APPROACH based on:

Variational evaluation of the finite temperature corrections by means of a Fermi – HyperNetted Chain calculation; Application of the corrections to theT=0 equation of state computed with the DDI

A. Yu. Illarionov, S. Gandolfi, K.E. Schmidt, S. Fantoni, N. Bassan, F.P.

Many electron systems

Topic: Rashba interactions/spin orbit(E. Lipparini, A. Ambrosetti, F.P.)

Electrons confined in a 2D quantum well are subject to the effect of an electric field E perpendicular to the plane containing the electrons if the confining potential is asymmetric

€

VRashba =λ

pixσ i

y − piyσ i

x[ ]i=1

N

∑ ∝ S ⋅ B

E v

B

S

Many electron systems

λ=0.2

λ=0.5

λ=0.1

N=58 rs=1 λ dependence of the energy

As expected the polarization increases with the strength of the electric field

N=58 rs=5

gs(r) (no Rashba)

gt(r) (no Rashba)

gs(r) (with Rashba)

gt(r) (with Rashba)

€

gc (r) = NΨδ( ri − rj )Ψ

Ψ Ψi< j∑

gσ (r) = NΨδ( ri − rj )

σ i ⋅ σ j Ψ

Ψ Ψi< j∑

gs(r) =14gc (r) − gt (r)[ ]

gs(r) =143gc (r) + gt (r)[ ]

It is possible to compute pair distribution functions in the spin-singlet and spin-triplet channels.

y component: broken symmetry

z component : circular symmetry

x component: broken symmetry

N=3 ω=0.28 λ=0.1

Future extensions

Atoms and solids (A. Ambrosetti, L. Mitas)

Ultracold Atoms

QMC Algortihms

Sign Problem (shall thou have no uncontrolled approximations....)

(M.H. Kalos, A. Roggero)Still work in progress. We are exploration the possibility that the plus/minus symmetry in the Diffusion Monte Carlo algorithm is broken by choosing a position-dependent dynamics of pairs of signed walkers.

PARALLEL DYNAMICS REFLECTED DYNAMICS

€

E0A ≈

ˆ H ΨTA (R+)

i∑ − ˆ H ΨT

A (R−)i∑

ΨTA (R+)

i∑ − ΨT

A (R−)i∑

“Exact” propagations can be performed in simple discretized models

QMC Algortihms

Inhomogeneous Fermion Systems(M.H. Kalos, F. Calcavecchia, F.P.)

Variational Monte Carlo calculations based on Shadow Wave Functions would be an extremely powerful method to address inhomogeneous Fermion matter (think of the NS crust). However, this algorithm suffers of a severe sign problem too.

12/16/11

V(R) Kinetic term

-lnφS(S) -lnφ (R)

K(R,S)

ΨTA (R) =Φr (R) K(R,S)∫ D↑ (S↑ )D↓ (S↓ )Φs(S)dS

€

ΨTA O(R)ΨT

A

ΨTA ΨT

A =1

ΨTA ΨT

A dRdSdS'O(R)ϕr(R)2Ξ(R,S,S') =∫∫∫

=1

ΨTA ΨT

A dRdSdS'O(R)ϕr(R)2 Ξ(R,S,S')Ξ(R,S,S')

Ξ(R,S,S') =∫∫∫

This is positive, and we can sample from it

This is a “weight” W(R,S,S’)=±1

peoplepeople interaction

Alessandro L., Omar (Crust)

Giampaolo (AFDMC for nuclei, wavefunctions)

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