Work statistics for sudden quenches in interacting quantum many-body systems

Classical theory of universal quantum work distribution in chaotic and disordered non-interacting Fermi systems

We present a universal theory of quantum work statistics in generic disordered non-interacting Fermi systems, displaying a chaotic single-particle spectrum captured by random matrix theory. We consider quantum quenches both within a driven random matrix formalism and in an experimentally accessible microscopic model, describing a two-dimensional disordered quantum dot. By extending Anderson’s orthogonality determinant formula to compute quantum work distribution, we demonstrate that work statistics is non-Gaussian and is characterized by a few dimensionless parameters. At longer times, quantum interference effects become irrelevant and the quantum work distribution is well-described in terms of a purely classical ladder model with a symmetric exclusion process in energy space, while bosonization and mean field methods provide accurate analytical expressions for the work statistics. Our results demonstrate the universality of work distribution in generic chaotic Fermi systems, captured by the analytical predictions of a mean field theory, and can be verified by calorimetric measurements on nanoscale circuits.

Work statistics and symmetry breaking in an excited-state quantum phase transition

We examine how the presence of an excited-state quantum phase transition manifests in the dynamics of a many-body system subject to a sudden quench. Focusing on the Lipkin-Meshkov-Glick model initialized in the ground state of the ferromagnetic phase, we demonstrate that the work probability distribution displays non-Gaussian behavior for quenches in the vicinity of the excited-state critical point. Furthermore, we show that the entropy of the diagonal ensemble is highly susceptible to critical regions, making it a robust and practical indicator of the associated spectral characteristics. We assess the role that symmetry breaking has on the ensuing dynamics, highlighting that its effect is only present for quenches beyond the critical point. Finally, we show that similar features persist when the system is initialized in an excited state and briefly explore the behavior for initial states in the paramagnetic phase.

Nonequilibrium Green's Function's Approach to the Calculation of Work Statistics

The calculation of work distributions in a quantum many-body system is of significant importance and also of formidable difficulty in the field of nonequilibrium quantum statistical mechanics. To solve this problem, inspired by the Schwinger-Keldysh formalism, we propose the contour-integral formulation for work statistics. Based on this contour integral, we show how to do the perturbation expansion of the characteristic function of work (CFW) and obtain the approximate expression of the CFW to the second order of the work parameter for an arbitrary system under a perturbative protocol. We also demonstrate the validity of fluctuation theorems by utilizing the Kubo-Martin-Schwinger condition. Finally, we use noninteracting identical particles in a forced harmonic potential as an example to demonstrate the powerfulness of our approach.