Superdiffusive quantum work and adiabatic quantum evolution in finite temperature chaotic Fermi systems

TL;DR

This paper analyzes the distribution of quantum work in disordered fermionic nanosystems at finite temperature, revealing Gaussian and non-Gaussian regimes, superdiffusive fluctuations, and universal behavior depending on work and temperature.

Contribution

It introduces an analytical determinant formula for work statistics in finite-temperature disordered fermionic systems and characterizes different fluctuation regimes and their universal aspects.

Findings

Work distribution is Gaussian for small work compared to thermal energy.

At low temperature or large work, non-Gaussian superdiffusive fluctuations emerge.

Work statistics follow a Markovian diffusion process, with universal behavior at large work.

Abstract

We study the full distribution of quantum work in generic, noninteracting, disordered fermionic nanosystems at finite temperature. We derive an analytical determinant formula for the characteristic function of work statistics for quantum quenches starting from a thermal initial state. For work small compared to the thermal energy of the Fermi gas, work distribution is Gaussian, and the variance of work is proportional to the average work, while in the low temperature or large work limit, a non-Gaussian distribution with superdiffusive work fluctuations is observed. Similarly, the time dependence of the probability of adiabaticity crosses over from an exponential to a stretched exponential behavior. For large enough average work, the work distribution becomes universal, and depends only on the temperature and the mean work. Apart from initial low temperature transients, work statistics are well captured by a Markovian energy-space diffusion process of hard-core particles, starting from a thermal initial state. Our findings can be verified by measurements on nanoscale circuits or via single qubit interferometry.