Work statistics, quantum signatures and enhanced work extraction in quadratic fermionic models

TL;DR

This paper investigates quantum corrections to work statistics in quadratic fermionic models, revealing non-classical signatures via Kirkwood-Dirac quasiprobabilities and demonstrating enhanced work extraction near critical points.

Contribution

It introduces a method to detect quantum corrections in work statistics using KDQ and relates non-classical behavior to criticality in the transverse-field Ising model.

Findings

Non-classical KDQ signatures appear at critical points.

Quantum corrections influence work extraction efficiency.

Negative and complex quasiprobabilities indicate non-classical regimes.

Abstract

In quadratic fermionic models we determine a quantum correction to the work statistics after a sudden and a time-dependent driving. Such a correction lies in the non-commutativity of the initial quantum state and the time-dependent Hamiltonian, and is revealed via the Kirkwood-Dirac quasiprobability (KDQ) approach to two-times correlators. Thanks to the latter, one can assess the onset of non-classical signatures in the KDQ distribution of work, in the form of negative and complex values that no classical theory can reveal. By applying these concepts on the one-dimensional transverse-field Ising model, we relate non-classical behaviours of the KDQ statistics of work in correspondence of the critical points of the model. Finally, we also prove the enhancement of the extracted work in non-classical regimes where the non-commutativity takes a role.