Quantum statistical effects in multi-channel wave packet scattering of non-interacting identical particles

TL;DR

This paper develops a generating function approach to analyze quantum statistical effects in multi-channel wave packet scattering of non-interacting identical particles, revealing how indistinguishability influences scattering statistics and correlations.

Contribution

It introduces a new method to evaluate scattering probabilities and correlations for identical particles, highlighting the impact of quantum statistics on scattering outcomes.

Findings

Indistinguishability affects single-channel statistics without changing mean particle numbers.

Bunching and anti-bunching behaviors are observable in extreme scattering cases.

Resonance in a cavity can lead to particle pile-up inside the scatterer.

Abstract

For a number of non-interacting identical particles entering a multi-channel scatterer in various wave packet states, we construct a generating function for the probabilities of various scattering outcomes. This is used to evaluate the mean numbers of particles $\overline{n}_m$ scattered into a given ($m$-th) channel, single-channel statistics, and inter-channel correlations. We show that for initially uncorrelated particles, indistinguishability changes single channel statistics without altering the the value of $\overline{n}_m$. For uncorrelated bosons and fermions, bunching and anti-bunching behaviour can be detected in the extreme-case probabilities, to have all particles scattered into the same channel, or none of particles scattered into a channel, or channels. As an example, we consider a cavity with a single long-lived resonance accessible to the particles, which allows them to "pile up" inside the scatterer.