Kolmogorov-type non-thermal fixed points and beyond of far-from-equilibrium dilute system: ultra-cold Fermi gas

TL;DR

The paper analyzes far-from-equilibrium dynamics of a spatially homogeneous, dilute ultra-cold Fermi gas by incorporating next-to-leading-order (NLO) quantum corrections through nonperturbative $1/N$-based resummations. Using the Schwinger-Keldysh formalism and Kadanoff-Baym transport equations, it demonstrates the existence of Kolmogorov-type non-thermal fixed points in the Boltzmann limit under a quasi-particle assumption, and derives associated scale-invariant flux exponents for particle and energy cascades. Beyond these fixed points, the work shows that off-shell $1\leftrightarrow 3$ processes and strong-coupling $1/N$ corrections can yield new stationary states with distinct scaling exponents, particularly in the high-momentum regime. The results connect non-equilibrium quantum field theory to experimentally accessible regimes in ultracold Fermi systems and provide concrete predictions for future simulations and measurements of far-from-equilibrium stationary states.

Abstract

The far-from-equilibrium dynamics driven by the scattering from next-to-leading-order (NLO) corrections in the quantum field theory has stationary solutions for the particle distribution characterized as the Kolmogorov-type non-thermal fixed points. The dynamics of the spatially homogeneous, isotropic dilute ultra-cold Fermi gas is investigated, and its kinetic equation confirms the Kolmogorov-type non-thermal fixed points in the perturbation theory by the quasi-particle assumption, in contrast to the wave turbulence of the weakly coupled ultra-cold Bose gas. In addition, other stationary states are found without the quasi-particle assumption and in a strongly coupled system. These analytical solutions provide chances for future experiments and numerical simulations in search of far-from-equilibrium stationary states of the dilute system.