Work Statistics, Loschmidt Echo and Information Scrambling in Chaotic Quantum Systems

TL;DR

This paper analyzes the work statistics of chaotic quantum systems under sudden quenches, linking it to Loschmidt echo dynamics and information scrambling, with exact results for arbitrary temperature and size.

Contribution

It provides an exact characterization of work statistics in chaotic quantum systems using random matrix theory, connecting it to Loschmidt echo and information scrambling measures.

Findings

Exact work distribution for chaotic systems under sudden quench.

Relation between work statistics and Loschmidt echo dynamics.

Insights into information scrambling via spectral form factor.

Abstract

Characterizing the work statistics of driven complex quantum systems is generally challenging because of the exponential growth with the system size of the number of transitions involved between different energy levels. We consider the quantum work distribution associated with the driving of chaotic quantum systems described by random matrix Hamiltonians and characterize exactly the work statistics associated with a sudden quench for arbitrary temperature and system size. Knowledge of the work statistics yields the Loschmidt echo dynamics of an entangled state between two copies of the system of interest, the thermofield double state. This echo dynamics is dictated by the spectral form factor. We discuss its relation to frame potentials and its use to assess information scrambling.