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.