Quantum work statistics in regular and classical-chaotic dynamical billiard systems

TL;DR

This paper compares classical and quantum work statistics in two-dimensional billiard systems, providing analytical and numerical insights into their correspondence and the nature of quantum work in small systems.

Contribution

It introduces a detailed analysis of work distributions in classical and quantum billiards, including analytical formulas and numerical results highlighting their similarities and differences.

Findings

Quantum and classical work distributions show interesting correlations.

Analytical formulas are derived for both systems.

Quantum results reveal unique features of work in small quantum systems.

Abstract

In the thermodynamics of nanoscopic systems the relation between classical and quantum mechanical description is of particular importance. To scrutinize this correspondence we have picked out two 2-dim billiard systems. Both systems are studied in the classical and the quantum mechanical setting. The classical conditional probability density $p(E,L|E_0,L_0)$ as well as the quantum mechanical transition probability $P(n,l|n_0,l_0)$ are calculated which build the basis for statistical analysis. We calculate the work distribution for a particle. Especially the results in the quantum case are of special interest since already a suitable definition of mechanical work in small quantum systems is controversial. Furthermore we analysed the probability of both zero work and zero angular momentum difference. Using connections to an exact solvable system analytical formulas are given in both systems. In the quantum case we get numerical results with some interesting relations to the classical case.