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arXiv:2410.10492 · Acta Physica Polonica B

Relaxation of Particle–Hole-type Excitation in a Fermi System Within the~Diffusion Approximation of Kinetic Theory for the Case of Constant Diffusion and Drift Coefficients

S. V. Lukyanov

Published Jan 1, 2025• 0 citations
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Abstract

The time evolution of the distribution function for a particle-hole excitation in a Fermi system was calculated using the direct numerical solution of a nonlinear diffusion equation in momentum space. A phenomenological expression for calculating the relaxation time of such an excitation to its equilibrium value has been proposed. It is shown that the relaxation time is dependent on both the excitation energy and the mass number.

DOI
10.5506/aphyspolb.56.1-a2

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The time evolution of the distribution function for a particle-hole excitation in a Fermi system was calculated using the direct numerical solution of a nonlinear diffusion equation in momentum space. A phenomenological expression for calculating the relaxation time of such an excitation to its equilibrium value has been proposed. It is shown that the relaxation time is dependent on both the excitation energy and the mass number.
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Motivated by the recent interest in nonequilibrium phenomena in quantum many-body systems, we study strongly interacting fermions on a lattice by deriving and numerically solving quantum Boltzmann equations that describe their relaxation to thermodynamic equilibrium. The derivation is carried out by inspecting the hierarchy of correlations within the framework of the 1/Z1/Z1/Z expansion. Applying the Markov approximation, we obtain the dynamic equations for the distribution functions. Interestingly, we find that in the strong-coupling limit, collisions between particles and holes dominate over particle-particle and hole-hole collisions---in stark contrast to weakly interacting systems. As a consequence, our numerical simulations show that the relaxation timescales strongly depend on the type of excitations (particles or holes or both) that are initially present.
Local kinetic equilibration is a prerequisite for hydrodynamics to be valid. Here it is described through a nonlinear diffusion equation for finite systems of fermions and bosons. The model is solved exactly for constant transport coefficients in both cases. It has the proper Fermi-Dirac and Bose-Einstein equilibrium limits and can replace the relaxation-time approximation (RTA). The microscopic transport coefficients are determined through the macroscopic variables temperature and local equilibration time. Applications to the transverse energy of quarks and gluons in the initial stages of central relativistic heavy-ion collisions, and to bosonic and fermionic atoms at low energies appropriate for cold quantum gases are discussed.