Decays of unstable quantum systems

TL;DR

This paper provides a comprehensive pedagogical overview of quantum decay processes, emphasizing the limitations of exponential decay models and introducing methods to analyze non-exponential decay phenomena in unstable quantum systems.

Contribution

It introduces general methods and elementary models for describing quantum decays, highlighting the breakdown of exponential decay approximations and exploring non-exponential decay regimes.

Findings

Analysis of conditions for exponential decay validity

Models for non-exponential decay due to resonance

Criteria for the breakdown of exponential decay approximation

Abstract

This paper is a pedagogical yet critical introduction to the quantum description of unstable systems, mostly at the level of a graduate quantum mechanics course. Quantum decays appear in many different fields of physics, and their description beyond the exponential approximation is the source of technical and conceptual challenges. In this article, we present both general methods that can be adapted to a large class of problems, and specific elementary models to describe phenomena like photo-emission, beta emission and tunneling-induced decays. We pay particular attention to the emergence of exponential decay; we analyze the approximations that justify it, and we present criteria for its breakdown. We also present a detailed model for non-exponential decays due to resonance, and an elementary model describing decays in terms of particle-detection probabilities. We argue that the traditional methods for treating decays face significant problems outside the regime of exponential decay, and that the exploration of novel regimes of current interest requires new tools.