Quantum corrections of work statistics in closed quantum systems

TL;DR

This paper explores quantum corrections to work statistics in closed quantum systems, establishing a semiclassical approximation and analyzing the physical origins of these corrections through explicit formulas and oscillator models.

Contribution

It introduces a semiclassical approximation for quantum work characteristic functions and derives explicit formulas for quantum corrections in powers of 5, clarifying their physical origins.

Findings

Quantum corrections appear in even powers of 5.

Explicit formulas for 5^2 corrections are derived.

Work characteristic functions are calculated for harmonic and quartic oscillators.

Abstract

We investigate quantum corrections to the classical work characteristic function (CF) as a semiclassical approximation to the full quantum work CF. In addition to explicitly establishing the quantum-classical correspondence of the Feynman-Kac formula, we find that these quantum corrections must be in even powers of $\hbar$. Exact formulas of the lowest corrections ($\hbar^2$) are proposed, and their physical origins are clarified. We calculate the work CFs for a forced harmonic oscillator and a forced quartic oscillator respectively to illustrate our results.