Classical Theory of Quantum Work Distribution in Chaotic Fermion Systems

TL;DR

This paper develops a theoretical framework for quantum work distribution in chaotic disordered Fermi systems, revealing non-Gaussian statistics and classical behavior at long times, validated by simulations and applicable to nanoscale experiments.

Contribution

It extends random matrix theory and mean field methods to analyze quantum work in chaotic fermion systems, providing analytical and numerical insights.

Findings

Work distribution is non-Gaussian and characterized by a few parameters.

At long times, quantum interference effects diminish, leading to classical behavior.

Predictions are validated by numerical simulations and applicable to nanoscale calorimetric measurements.

Abstract

We present a theory of quantum work statistics in generic chaotic, disordered Fermi liquid systems within a driven random matrix formalism. By extending P. W. Anderson's orthogonality determinant formula to compute quantum work distribution, we find that work statistics is non-Gaussian and is characterized by a few dimensionless parameters. At longer times, quantum interference effects become irrelevant and the quantum work distribution is well-described in terms of a purely classical ladder model with a symmetric exclusion process in energy space, while bosonization and mean field methods provide accurate analytical expressions for the work statistics. Our random matrix and mean field predictions are validated by numerical simulations for a two-dimensional disordered quantum dot, and can be verified by calorimetric measurements on nanoscale circuits.