Quantum corrections of work statistics in closed quantum systems

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 $\hslash$. Exact formulas of the lowest corrections (${\hslash }^2$) 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.

Phys.Rev.E, in press

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• Quantum-classical correspondence principle for heat distribution in quantum Brownian motion
• Computing characteristic functions of quantum work in phase space
• Energy conservation and fluctuation theorem are incompatible for quantum work
• Hierarchical structure of fluctuation theorems for a driven system in contact with multiple heat reservoirs
• Quantum corrections to the entropy and its application in the study of quantum Carnot engines
• Semi-classical work and quantum work identities in Weyl representation
• Symmetry and its breaking in path integral approach to quantum Brownian motion
• Path integral approach to the calculation of the characteristic function of work
• Superdiffusive quantum work and adiabatic quantum evolution in finite temperature chaotic Fermi systems
• Energy exchange statistics and fluctuation theorem for non-thermal asymptotic states