q-deformed fermion in many-particle systems and its application to BCS theory

Abstract

In recent decades, there have been increasing interests in quantum statistics beyond the standard Fermi-Dirac and Bose-Einstein statistics, such as the fractional statistics, quon statistics, anyon statistics and quantum groups, since they can provide some new insights into the cosmology, nuclear physics and condensed matter. In this paper, we study the many-particle system formed by the q-deformed fermions (q-fermion), which is realized by deforming the quantum algebra of the anticommutation relations. We investigate from a standard perspective of the finite temperature field theory and try to construct the finite temperature Green's function formalism for the free many-q-fermion system, then generalize it to the well known interacting fermionic system, the superconductor, and finally obtain a consistent q-deformed BCS (qBCS) theory. At low temperature, this theory predicts a Sarma-like ordered phase, and we call it the q-deformed Sarma phase. It also presents a symmetric phase diagram in the parameter space and new thermodynamic relations.

Finite temperature behaviors of q-deformed Fermi gases

“…At zero temperature, the behaviors in the BCS regimes (or a superconducting model) has been studied in ref. [53]. It has been found that the breached T c as a function of 1/(k F a) of polarized q-Fermi gases with either fixed q or p. In the left panel, q is fixed to be 0.5, while in the right panel p is fixed to be 0.6.…”

“…For details, please refer to Ref. [53]. At very low temperature, we self-consistently assume that the pairing between q-fermions with different spins may occur and lead to the fermionic condensation.…”

“…In this paper, we only focus on the s-wave paring, of which the pairing function is given by ∆(x) = g ψ ↑ (x)ψ ↓ (x) with g being the inter-particle coupling constant. Assuming the chemical potentials for each species are µ ↑,↓ , and the particle mass is m, the Hamiltonian of the qBCS model is generalized to take the form [53]…”

“…In Ref. [53], we construct an exact solvable q-deformed BCS (qBCS) theory by generalizing the temperature Green's function formalism to the two-component many-q-fermion system. When q = 1, it naturally reduces to the ordinary BCS theory.…”

Thermostatistics of a q -deformed relativistic ideal Fermi gas

“…There have been intensive studies on the ideal many-quon systems [34][35][36][37][38][39][40][41][42][43][44]. In our recent paper [45], we successfully constructed a q-deformed many-body theory, the q-deformed BCS theory, for the most famous interacting fermionic system, the superconductor. By applying it to the q-deformed interacting Fermi gases, we obtained some interesting physical predictions [46].…”