A quantum relaxation-time approximation for finite fermion systems

TL;DR

This paper introduces a quantum relaxation-time approximation within time-dependent density functional theory to model the dynamics of strongly excited fermion systems, capturing dissipation effects in various dynamical regimes.

Contribution

It develops a quantum relaxation approximation based on semi-classical relaxation times, enabling more accurate modeling of dissipation in excited fermion systems.

Findings

Dissipation significantly affects ionization and electron emission distributions.

The method effectively models energy dissipation in both linear and non-linear regimes.

Relaxation times derived from semi-classical experience are applicable in quantum simulations.

Abstract

We propose a relaxation time approximation for the description of the dynamics of strongly excited fermion systems. Our approach is based on time-dependent density functional theory at the level of the local density approximation. This mean-field picture is augmented by collisional correlations handled in relaxation time approximation which is inspired from the corresponding semi-classical picture. The method involves the estimate of microscopic relaxation rates/times which is presently taken from the well established semi-classical experience. The relaxation time approximation implies evaluation of the instantaneous equilibrium state towards which the dynamical state is progressively driven at the pace of the microscopic relaxation time. As test case, we consider Na clusters of various sizes excited either by a swift ion projectile or by a short and intense laser pulse, driven in various dynamical regimes ranging from linear to strongly non-linear reactions. We observe a strong effect of dissipation on sensitive observables such as net ionization and angular distributions of emitted electrons. The effect is especially large for moderate excitations where typical relaxation/dissipation time scales efficiently compete with ionization for dissipating the available excitation energy. Technical details on the actual procedure to implement a working recipe of such a quantum relaxation approximation are given in appendices for completeness.