Quantum First Passage Time Problem-A Bohmian Perspective

TL;DR

This paper uses Bohmian mechanics to analyze the quantum first passage time problem, deriving an empirical distribution and discussing its implications for quantum theory foundations.

Contribution

It introduces a Bohmian mechanics-based approach to derive the first passage time distribution in quantum systems, addressing a longstanding open problem.

Findings

Derived empirical passage time distribution $\Pi( au)$

Provided insights into quantum arrival time predictions

Discussed implications for quantum theory foundations

Abstract

The prediction of arrival time or first passage time statistics of a quantum particle is an open problem, which challenges the foundations of quantum theory. One of the most promising and insightful approaches to this problem stems from the de Broglie-Bohm pilot-wave theory (a.k.a Bohmian mechanics). Applying the fundamental postulates of this theory, we analyze a simplified first passage time experiment and derive the empirical passage time distribution $\Pi(\tau)$. Implications of our results are also discussed.