BCS BEC crossover and phase structure of relativistic system: a variational approach

Abstract

We investigate here the BCS BEC crossover in relativistic systems using a variational construct for the ground state and the minimization of the thermodynamic potential. This is first studied in a four fermion point interaction model and with a BCS type ansatz for the ground state with fermion pairs. It is shown that the antiparticle degrees of freedom play an important role in the BCS BEC crossover physics, even when the ratio of fermi momentum to the mass of the fermion is small. We also consider the phase structure for the case of fermion pairing with imbalanced populations. Within the ansatz, thermodynamically stable gapless modes for both fermions and anti fermions are seen for strong coupling in the BEC regime. We further investigate the effect of fluctuations of the condensate field by treating it as a dynamical field and generalize the BCS ansatz to include quanta of the condensate field also in a boson fermion model with quartic self interaction of the condensate field. It is seen that the critical temperature decreases with inclusion of fluctuations.

18 pages, 13 figures, one more section added, title modified, version to appear in Phys Rev D

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• BCS-BEC crossover in relativistic Fermi systems
• Magnetic Tuning of the Relativistic BCS-BEC Crossover
• Non-Hermitian BCS-BEC crossover of Dirac fermions
• Relativistic BCS-BEC crossover of a two-species Fermi gas with number density asymmetry at zero temperature
• Optimized perturbation theory applied to the study of the thermodynamics and BEC-BCS crossover in the three-color Nambu--Jona-Lasinio model
• BCS-BEC Crossover and Stability in a Nambu-Jona-Lasinio Model with Diquark-Diquark Repulsion
• Equation of State in a Strongly Interacting Relativistic System
• Diquarks in the nilpotency expansion of QCD and their role at finite chemical potential
• Chiral symmetry breaking and quark confinement in the nilpotency expansion of QCD
• $K^{-}d\to \pi \Sigma n$ reactions and structure of the $\Lambda (1405)$
• Some recent progress on quark pairings in dense quark and nuclear matter
• Pairing fluctuation effects in a strongly coupled color superfluid/superconductor