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.
Highlights
The response to a sudden change in the Hamiltonian is a topic which has led to many valuable insights into the physics of quantum many-particle systems in recent years
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
Since the work probability distribution is related to the delocalization of the initial state in the Hilbert space defined by the eigenstates of the final Hamiltonian, it is natural to characterize this further by investigating the delocalization dynamics
Summary
The response to a sudden change in the Hamiltonian is a topic which has led to many valuable insights into the physics of quantum many-particle systems in recent years. 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.
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