Quantum work statistics in regular and classicalchaotic dynamical billiard 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 chosen two twodimensional billiard systems. Both systems are studied in the classical and the quantum mechanical settings. 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 the statistical analysis. We calculate the work distribution for one particle. The results in the quantum case in particular are of special interest since a suitable definition of mechanical work in small quantum systems is already controversial. Furthermore, we analyze the probability of both zero work and zero angular momentum difference. Using connections to an exactly solvable system analytical formulas are given for both systems. In the quantum case we get numerical results with some interesting relations to the classical case.
 Publication:

Physical Review E
 Pub Date:
 May 2022
 DOI:
 10.1103/PhysRevE.105.054147
 arXiv:
 arXiv:2111.14383
 Bibcode:
 2022PhRvE.105e4147R
 Keywords:

 Nonlinear Sciences  Chaotic Dynamics;
 Condensed Matter  Statistical Mechanics
 EPrint:
 doi:10.1103/PhysRevE.105.054147