Fluctuation effect in relativistic Fluctuation effect in relativistic BCS BCS - - BEC BEC Crossover Crossover Jian Deng, Department of Modern Physics, USTC Jian Deng, Department of Modern Physics, USTC 2008, 7, 12 @ QCD workshop, Hefei 2008, 7, 12 @ QCD workshop, Hefei Introduction Boson-fermion model for BCS-BEC crossover beyond MFA, fluctuation effect Discussions and outlooks • J. Deng, A. Schmitt, Q. Wang, Phys.Rev.D76:034013,2007 • J. Deng, J.-C. Wang, Q. Wang, arXiv:0803.4360 • J. Deng et al., in preparation
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Fluctuation effect in relativistic BCS-BEC Crossover Jian Deng, Department of Modern Physics, USTC 2008, 7, 12 @ QCD workshop, Hefei Introduction Boson-fermion.
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Fluctuation effect in relativistic Fluctuation effect in relativistic BCSBCS--BECBEC Crossover Crossover
Jian Deng, Department of Modern Physics, USTCJian Deng, Department of Modern Physics, USTC
Shadowed region stand for unstable Shadowed region stand for unstable solutions, which will collapse to solutions, which will collapse to LOFF LOFF
statestate or or separating phaseseparating phaseWilfgang Ketterle (MIT) arXiv:0805.0623 Wilfgang Ketterle (MIT) arXiv:0805.0623 Realization of a strongly interacting Realization of a strongly interacting Bose-Bose-
Fermi mixtureFermi mixture from a two-component from a two-component Fermi gasFermi gas
BeyondBeyond MFAMFA
The fluctuation of The fluctuation of condensate sets in condensate sets in
Higgs Higgs andand Nambu-Nambu-
GoldstoneGoldstone fields:fields:
The The CJTCJT formalism formalism (J. M. (J. M. CCornwall, R. ornwall, R. JJackiw and E. ackiw and E. TTomboulis, 1974 )omboulis, 1974 )
Full Full propagator:propagator:Tree-level Tree-level
propagator:propagator:
2PI 2PI diagrams and diagrams and DSDS equations equations
Pseudo-Pseudo-gapgap
First order phase First order phase transition with transition with
fixed chemical potentialfixed chemical potential
Introduction of term in : Introduction of term in :
B.I.Halperin, T.C.Lubensky and S. Ma 1974B.I.Halperin, T.C.Lubensky and S. Ma 1974 (magnetic field fluctuations)(magnetic field fluctuations)I. Giannakis, D. f. Hou, H. c. Ren and D. H. Rischke, 2004I. Giannakis, D. f. Hou, H. c. Ren and D. H. Rischke, 2004 ((Gauge Field Fluctuations)Gauge Field Fluctuations)Sasaki, Friman, Redlich, 2007Sasaki, Friman, Redlich, 2007 (baryon number fluctuation in 1st chiral phase transition)(baryon number fluctuation in 1st chiral phase transition)
gap and density gap and 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.
T-dependenceT-dependence
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.
Summary Summary
1. Relativistic boson-fermion model can well 1. Relativistic boson-fermion model can well describe the describe the BCSBCS- - BECBEC crossover within or crossover within or beyond beyond MFAMFA..
2.As an fluctuation effect, the pseudo-gap become more important for larger temperature.
3.3.FluctuationFluctuation changes the phase transition to be changes the phase transition to be first-orderfirst-order..
Outlook Outlook Full self-consistencyFull self-consistency is needed. is needed.
BEC criterionBEC criterion for interacting bosons need more for interacting bosons need more close look.close look.
Anti-particlesAnti-particles and and finite size of bosonsfinite size of bosons should should be be considered carefullyconsidered carefully
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 ).
Thanks a Thanks a lotlot
BEC: BEC: condensate, number density condensate, number density conservation,conservation,
critical temperaturecritical temperature
Distribution Distribution function:function:
Density Density conservation:conservation:
Thermal bosons at Thermal bosons at most:most:
Temperature Temperature dependence:dependence:
BosonBoson--fermionfermion model model ((MFAMFA))With With bosonicbosonic and and fermionicfermionic degrees of degrees of
freedom and their coupling, but neglect freedom and their coupling, but neglect the coupling of thermal bosons and the coupling of thermal bosons and
fermions as fermions as MMean ean FField ield AApproximation pproximation
Pairing with imbalance Pairing with imbalance population population
Fermi surface Fermi surface topologies topologies
ApproximatioApproximationn
Ensure the reliability of gap Ensure the reliability of gap equationequation
Continuous changing of Continuous changing of gap with fixed number gap with fixed number
densitydensity
But still But still first-orderfirst-order phase phase transitiontransition