Detection Time Distribution for Several Quantum Particles

TL;DR

This paper extends the absorbing boundary rule for calculating detection time distributions from one quantum particle to multiple particles, incorporating wave function collapse upon detection and adapting to moving detectors.

Contribution

It introduces a natural extension of the absorbing boundary rule to n-particle systems with wave function collapse and moving detectors.

Findings

Extension of the absorbing boundary rule to multiple particles.

Inclusion of wave function collapse at detection events.

Adaptation of the rule for moving detectors.

Abstract

We address the question of how to compute the probability distribution of the time at which a detector clicks, in the situation of $n$ non-relativistic quantum particles in a volume $\Omega\subset \mathbb{R}^3$ in physical space and detectors placed along the boundary $\partial \Omega$ of $\Omega$. We have previously [arXiv:1601.03715] argued in favor of a rule for the 1-particle case that involves a Schr\"odinger equation with an absorbing boundary condition on $\partial \Omega$ introduced by Werner; we call this rule the "absorbing boundary rule." Here, we describe the natural extension of the absorbing boundary rule to the $n$-particle case. A key element of this extension is that, upon a detection event, the wave function gets collapsed by inserting the detected position, at the time of detection, into the wave function, thus yielding a wave function of $n-1$ particles. We also describe an extension of the absorbing boundary rule to the case of moving detectors.