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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…
Based on the Bogoliubov non-ideal gas model, we discuss the energy spectrum and phase transition of the superfluid Fermi gas of atoms with a weak attractive interaction on the canonical noncommutative space. Because the interaction of a…
We study the mass imbalanced Fermi-Fermi mixture within the framework of a two-dimensional lattice fermion model. Based on the thermodynamic and species dependent quasiparticle behavior we map out the finite temperature phase diagram of…
We study ultracold superfluid Bose-Fermi mixtures in three dimensions, with stronger confinement along one or two directions, using a non-perturbative beyond-mean-field model for bulk chemical potential valid along the weak-coupling to…
Superconductivity and superfluidity of fermions require, within the BCS theory, matching of the Fermi energies of the two interacting Fermion species. Difference in the number densities of the two species leads either to a normal state, to…
Ultra-cold atom experiments offer the unique opportunity to study mixing of different types of superfluid states. Our interest is in superfluid mixtures comprising particles with different statistics- Bose and Fermi. Such scenarios occur…
The superfluidity and pairing phenomena in ultracold atomic Fermi gases have been of great interest in recent years, with multiple tunable parameters. Here we study the BCS-BEC crossover behavior of balanced two-component Fermi gases in a…
We review the non-zero temperature relaxational dynamics of quantum systems near a zero temperature, second-order phase transition. We begin with the quantum Ising chain, for which universal and exact results for the relaxation rates can be…
The functional renormalisation group is used for the BCS-BEC crossover in gases of ultracold fermionic atoms. In a simple truncation, we see how universality and an effective theory with composite bosonic di-atom states emerge. We obtain a…
We briefly discuss recent experiments on the BCS-BEC crossover with ultracold alkali-metal atoms both in three-dimensional configurations and two-dimensional ones. Then we analyze the quantum-field-theory formalism used to describe an…
We review the study of the superfluid phase transition in a system of fermions whose interaction can be tuned continuously along the crossover from Bardeen-Cooper-Schrieffer (BCS) superconducting phase to a Bose-Einstein condensate (BEC),…
We developed a comprehensive semiclassical theory of solitons in one dimensional systems at BCS-BEC crossover to provide a semiclassical explanation of their excitation spectra. Our semiclassical results agree well with the exact solutions…
We analyze the accuracy of BCS-based approximations for calculating correlation energies and odd-even energy differences in 2-component fermionic systems with a small number of pairs. The analysis is focused on comparing BCS and projected…
We investigate the impact of higher-order fermionic deformations in phase transitions analogous to those described by the Bardeen-Cooper-Schrieffer (BCS) theory. Focusing specifically on the 8-fermion interaction, we show that this term can…
We examine the effect of the trapping potential on the critical temperature, $T_C$, for the BCS transition to a superfluid state in trapped atomic gases of fermions. $T_C$ for an arbitrary power law trap is calculated in the Thomas-Fermi…
The role of fluctuations is enhanced in lower dimensionality systems: in a two dimensions off-diagonal long-range order is destroyed by the fluctuations at any finite temperature, drastically modifying the critical properties with respect…
Quench dynamics of fermionic superfluids are an active topic both experimentally and theoretically. Using the BCS theory, such non-equilibrium problems can be reduced to nearly independent spin dynamics, only with a time-dependent…
In this chapter the recent theoretical work on phase transition in imbalanced fermion superfluids is reviewed. The imbalanced systems are those in which the two fermionic species candidate to form pairing have different Fermi surfaces or…
We investigate the phase diagram and the BCS-BEC crossover of a homogeneous three-component ultracold Fermi gas with a U(3) invariant attractive interaction. We show that the system at sufficiently low temperatures exhibits population…
Fermion systems with more than two components can exhibit pairing condensates of much more complex structure than the well-known single BCS condensate of spin-up and spin-down fermions. In the framework of the exactly solvable SO(8)…