Mean first-passage time of quantum transition processes

TL;DR

This paper introduces a quantum mean first-passage time (MFPT) framework, adapting statistical mechanics methods to analyze transition times in quantum systems, with applications to atomic and laser processes.

Contribution

It develops a novel approach for calculating quantum MFPTs by applying statistical mechanics techniques to quantum transition processes.

Findings

MFPT calculated for multi-state quantum systems

Analysis of environment-influenced transition processes

Application to hydrogen atom transitions and laser theory

Abstract

In this paper, we consider the problem of mean first-passage time (MFPT) in quantum mechanics; the MFPT is the average time of the transition from a given initial state, passing through some intermediate states, to a given final state for the first time. We apply the method developed in statistical mechanics for calculating the MFPT of random walks to calculate the MFPT of a transition process. As applications, we (1) calculate the MFPT for multiple-state systems, (2) discuss transition processes occurring in an environment background, (3) consider a roundabout transition in a hydrogen atom, and (4) apply the approach to laser theory.