On a Derivation of the Absorbing Boundary Rule

Abstract

Consider detectors waiting for a quantum particle to arrive at a surface $S$ in 3-space. For predicting the probability distribution of the time and place of detection, a rule was proposed in [arXiv:1601.03715], called the absorbing boundary rule (ABR) and involving a 1-particle Schrödinger equation with an absorbing boundary condition on $S$. While plausibility arguments for the ABR were given there, it would be desirable to derive the ABR from a microscopic model of a detector. We outline here such a derivation by putting together known results from the literature. Our derivation is non-rigorous, and it would still be desirable to have a rigorous version of it in the future.

arXiv comment6 pages LaTeX, no figures

References in corpus (8)

• Continuous quantum measurement and Itô formalism
• On Spontaneous Wave Function Collapse and Quantum Field Theory
• Quantum Dynamics under continuous projective measurements: non-Hermitian description and the continuous space limit
• Distribution of the Time at Which an Ideal Detector Clicks
• Detection Time Distribution for Several Quantum Particles
• Arrival Times Versus Detection Times
• The appearance of particle tracks in detectors
• Absorbing Boundary Condition as Limiting Case of Imaginary Potentials

Cited by in corpus (5)

• Arrival Times Versus Detection Times
• Existence of Schrodinger Evolution with Absorbing Boundary Condition
• Inequivalence of stochastic and Bohmian arrival times in time-of-flight experiments
• Absorbing detectors meet scattering theory
• A solution of the quantum time of arrival problem via mathematical probability theory