# Work distributions for random sudden quantum quenches

## TL;DR

This paper analyzes the statistical distribution of work done during sudden quantum quenches modeled by Gaussian unitary ensembles, deriving explicit formulas for two-level systems and limits for more complex cases.

## Contribution

It introduces a model for random quantum quenches using GUE matrices and derives the work distribution functions for specific cases, advancing understanding of quantum thermodynamics.

## Key findings

- Derived the work distribution for two-level systems.
- Obtained explicit work pdfs for quenches between GUE Hamiltonians at temperature limits.
- Provided a framework for analyzing work statistics in random quantum quenches.

## Abstract

The statistics of work performed on a system by a sudden random quench is investigated. Considering systems with finite dimensional Hilbert spaces we model a sudden random quench by randomly choosing elements from a Gaussian unitary ensemble (GUE) consisting of hermitean matrices with identically, Gaussian distributed matrix elements. A probability density function (pdf) of work in terms of initial and final energy distributions is derived and evaluated for a two-level system. Explicit results are obtained for quenches with a sharply given initial Hamiltonian, while the work pdfs for quenches between Hamiltonians from two independent GUEs can only be determined in explicit form in the limits of zero and infinite temperature.