Relation between quantum dwell times and flux-flux correlations

TL;DR

This paper explores the relationship between quantum dwell times and flux-flux correlations, showing that certain moments of the flux-flux correlation function match dwell-time moments, revealing quantum-specific behavior.

Contribution

It establishes a connection between flux-flux correlations and quantum dwell times, highlighting the quantum nature of the second moment and its difference from classical predictions.

Findings

First and second moments of flux-flux correlations match dwell-time moments.

Third and higher moments do not agree, indicating quantum effects.

Second moment is larger than classical counterpart, even for free particles.

Abstract

We examine the connection between the dwell time of a quantum particle in a region of space and flux-flux correlations at the boundaries. It is shown that the first and second moments of a flux-flux correlation function which generalizes a previous proposal by Pollak and Miller [E. Pollak and W. H. Miller, Phys. Rev. Lett. {\bf 53}, 115 (1984)], agree with the corresponding moments of the dwell-time distribution, whereas the third and higher moments do not. We also discuss operational approaches and approximations to measure the flux-flux correlation function and thus the second moment of the dwell time, which is shown to be characteristically quantum, and larger than the corresponding classical moment even for freely moving particles.