Group-theoretical approach to the calculation of quantum work distribution

TL;DR

This paper introduces a universal group-theoretical method to efficiently compute work distributions in quantum systems with quadratic Hamiltonians during arbitrary nonequilibrium processes, enabling exact solutions in several models.

Contribution

The authors develop a novel group-representation theory-based approach for calculating quantum work distributions, applicable to a wide class of quadratic Hamiltonian systems.

Findings

Exact solutions for work distributions in time-dependent harmonic oscillators

Analytical results for the dynamical Casimir effect

Work distribution calculations for the transverse XY model

Abstract

Usually the calculation of work distributions in an arbitrary nonequilibrium process in a quantum system, especially in a quantum many-body system is extremely cumbersome. For all quantum systems described by quadratic Hamiltonians, we invent a universal method for solving the work distribution of quantum systems in an arbitrary driving process by utilizing the group-representation theory. This method enables us to efficiently calculate work distributions where previous methods fail. In some specific models, such as the time-dependent harmonic oscillator, the dynamical Casimir effect, and the transverse XY model, the exact and analytical solutions of work distributions in an arbitrary nonequilibrium process are obtained. Our work initiates the study of quantum stochastic thermodynamics based on group-representation theory.