Connecting Scrambling and Work Statistics for Short-Range Interactions in the Harmonic Oscillator

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.

Automated summary

This study investigates the relationship between information scrambling and work statistics for short-range interacting particles in a one-dimensional harmonic trap. It finds that scrambling requires finite interactions and establishes a connection between scrambling properties and induced work fluctuations, which are directly observable in modern cold-atom experiments.