BCS-BEC crossover and phase structure of relativistic systems: 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.

Optimized perturbation theory applied to the study of the thermodynamics and BEC-BCS crossover in the three-color Nambu–Jona-Lasinio model

“…Note that from Eqs. (5.8) and (5.10), we obtain the simple relation betweenη and σ c in the vacuum:η 13) which shows that in the large-N c limit we reproduce the resultη = σ c as expected in the LN approximation.…”

“…Several works (see, e.g., Refs. [10][11][12]17]) show that it is possible for the condensate of diquarks initially to form a BEC phase, before the system goes to the BCS state, as we increase the baryon chemical potential going through this BEC-BCS crossover [13,14,16]. Some possible observational signatures for the BCS regime and the possibility of coexistence of the chiral and diquark phases have been explored in the literature [19], while a connection with hightemperature superconductors and a possible pseudogap was studied in Refs.…”

Pseudo-critical enhancement of thermal photons in relativistic heavy-ion collisions?

“…One option to increase thermal radiation in URHICs is a decrease of the thermalization time, τ 0 , of the medium, as investigated, e.g., in Refs. [46,9,47]. While the total yield generally increases above q T > 1 GeV, its slope becomes harder and the total v 2 becomes smaller, both not favored by the data.…”

Singular values of the Dirac operator in dense QCD-like theories

“…This phenomenon is called (relativistic) BEC-BCS crossover. It passes a number of nontrivial tests [21,22,26], and its possible realization in dense quark matter in QCD has been investigated in various model calculations [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42] (see also [43][44][45][46][47][48] for related models). In view of the known relation between ∆ and the Dirac eigenvalues [12,15], a natural question arises: How is the diquark condensate ψψ reflected in the 3 To evade the sign problem, one has to assume an even number of flavors with degenerate quark masses in the β = 1 and β = 2 cases.…”