Statistics of delay times in mesoscopic systems as a manifestation of eigenfunction fluctuations

TL;DR

This paper establishes a direct link between delay time statistics in mesoscopic systems and eigenfunction fluctuations, enabling experimental probing of eigenstates through delay measurements.

Contribution

It introduces a general explicit relation connecting delay time statistics with eigenfunction intensities in mesoscopic samples of any dimension.

Findings

Derived the probability density of partial delay times for multiple channels in quasi-1D systems.

Showed that delay times can serve as sensitive probes of eigenfunction fluctuations.

Provided a theoretical framework applicable to various spatial dimensions.

Abstract

We reveal a general explicit relation between the statistics of delay times in one-channel reflection from a mesoscopic sample of any spatial dimension and the statistics of the eigenfunction intensities in its closed counterpart. This opens a possibility to use experimentally measurable delay times as a sensitive probe of eigenfunction fluctuations. For the particular case of quasi-one dimensional geometry of the sample we use an alternative technique to derive the probability density of partial delay times for any number of open channels.