Connecting scrambling and work statistics for short-range interactions in the harmonic oscillator

TL;DR

This paper explores the link between information scrambling and work statistics in a one-dimensional harmonic trap with short-range interactions, revealing that scrambling correlates with work fluctuations measurable in cold atom experiments.

Contribution

It demonstrates a direct proportionality between the long-time average of the squared commutator and work variance in short-range interacting particles, connecting theoretical scrambling with experimental observables.

Findings

Scrambling requires finite interactions.

Long-time average of squared commutator is proportional to work variance.

Work fluctuations are experimentally accessible in cold atom setups.

Abstract

We investigate the relationship between information scrambling and work statistics after a quench for the paradigmatic example of short-range interacting particles in a one-dimensional harmonic trap, considering up to five particles numerically. In particular, we find that scrambling requires finite interactions, in the presence of which the long-time average of the squared commutator for the individual canonical operators is directly proportional to the variance of the work probability distribution. In addition to the numerical results, we outline the mathematical structure of the N-body system which leads to this outcome. We thereby establish a connection between the scrambling properties and the induced work fluctuations, with the latter being an experimental observable that is directly accessible in modern cold atom experiments.