Nonperturbative Analysis of a Quantum Mechanical Model for Unstable Particles

TL;DR

This paper provides a non-perturbative analysis of quantum decay in a particle-in-potential system, revealing exponential decay transitioning to power-law decay over time, applicable to both attractive and repulsive potentials.

Contribution

It offers a detailed non-perturbative study of unstable quantum states, explicitly calculating decay behaviors and power-law terms as functions of the coupling, extending understanding beyond perturbative methods.

Findings

Exponential decay observed for intermediate times.

Transition to power-law decay at long times.

Decay behavior consistent for both attractive and repulsive potentials.

Abstract

We present a detailed non-perturbative analysis of the time-evolution of a well-known quantum-mechanical system - a particle between potential walls - describing the decay of unstable states. For sufficiently high barriers, corresponding to unstable particles with large lifetimes, we find an exponential decay for intermediate times, turning into an asymptotic power decay. We explicitly compute such power terms in time as a function of the coupling in the model. The same behavior is obtained with a repulsive as well as with an attractive potential, the latter case not being related to any tunnelling effect.