Quantum to classical transition in the work distribution for chaotic systems

TL;DR

This paper introduces a semiclassical approximation for the work distribution in chaotic quantum systems undergoing a quench, bridging quantum and classical descriptions and improving understanding of nonequilibrium thermodynamics.

Contribution

It develops a new semiclassical method based on the dephasing representation and quantum ergodic conjecture to approximate quantum work distributions in chaotic systems.

Findings

Semiclassical approximation accurately describes quantum work distribution at higher temperatures.

The approach links quantum and classical work distributions.

The method is effective for chaotic systems undergoing a quench.

Abstract

The work distribution is a fundamental quantity in nonequilibrium thermodynamics mainly due to its connection with fluctuations theorems. Here we develop a semiclassical approximation to the work distribution for a quench process in chaotic systems. The approach is based on the dephasing representation of the quantum Loschmidt echo and on the quantum ergodic conjecture, which states that the Wigner function of a typical eigenstate of a classically chaotic Hamiltonian is equidistributed on the energy shell. We show that our semiclassical approximation is accurate in describing the quantum distribution as we increase the temperature. Moreover, we also show that this semiclassical approximation provides a link between the quantum and classical work distributions.