Statistics of work distribution in periodically driven closed quantum systems

TL;DR

This paper investigates the statistical properties of work distribution in periodically driven quantum systems, revealing universal bounds and oscillatory behaviors linked to quantum critical points, with implications for experimental verification.

Contribution

It introduces a universal lower bound for the rate function of work distribution and analyzes oscillatory features due to Stuckelberg interference in driven quantum systems.

Findings

Rate function satisfies a universal lower bound after integer periods.

Work distribution exhibits oscillations from Stuckelberg interference.

Results applicable to integrable models and experimentally testable.

Abstract

We study the statistics of the work distribution $P(w)$ in a $d-$dimensional closed quantum system with linear dimension $L$ subjected to a periodic drive with frequency $\omega_0$. We show that after an integer number of periods of the drive, the corresponding rate function $I(w)= -\ln[P(w)]/L^d$ satisfies an universal lower bound $I(0)\ge n_d$ and has a zero at $w=Q$, where $n_d$ and $Q$ are the defect density and residual energy generated during the drive. We supplement our results by calculating $I(w)$ for a class of $d$-dimensional integrable models and show that it has oscillatory dependence on $\omega_0$ originating from Stuckelberg interference generated during multiple passage through intermediate quantum critical points or regions during the drive. We suggest experiments to test our theory.