# Particle-number scaling of the quantum work statistics and Loschmidt echo in Fermi gases with time-dependent traps

## TL;DR

This paper studies how the particle number affects the out-of-equilibrium quantum dynamics of Fermi gases under time-dependent traps, revealing power-law behaviors and the robustness of these laws against interactions.

## Contribution

It provides a detailed analysis of particle-number scaling laws for quantum work and Loschmidt echo in Fermi gases, including effects of interactions and different dimensions.

## Key findings

- Power-law dependence of quantum work statistics on particle number.
- Loschmidt echo decay characterized by specific power laws.
- Interactions do not significantly alter the particle-number scaling laws.

## Abstract

We investigate the particle-number dependence of some features of the out-of-equilibrium dynamics of d-dimensional Fermi gases in the dilute regime. We consider protocols entailing the variation of the external potential which confines the particles within a limited spatial region, in particular sudden changes of the trap size. In order to characterize the dynamic behavior of the Fermi gas, we consider various global quantities such as the ground-state fidelity for different trap sizes, the quantum work statistics associated with the protocol considered, and the Loschmidt echo measuring the overlap of the out-of-equilibrium quantum states with the initial ground state. Their asymptotic particle-number dependences show power laws for noninteracting Fermi gases. We also discuss the effects of short-ranged interactions to the power laws of the average work and its square fluctuations, within the Hubbard model and its continuum limit, arguing that they do not generally change the particle-number power laws of the free Fermi gases, in any spatial dimensions.