Solvable models of resonances and decays

TL;DR

This paper reviews solvable quantum models, from classical Friedrichs results to quantum graphs, to understand resonance and decay phenomena through analytical methods and dynamical mechanisms.

Contribution

It provides a comprehensive survey of solvable models in quantum resonance and decay, highlighting recent advances in quantum graph theory.

Findings

Analysis of classical Friedrichs model

Recent developments in quantum graph theory

Insights into dynamical mechanisms of resonances

Abstract

Resonance and decay phenomena are ubiquitous in the quantum world. To understand them in their complexity it is useful to study solvable models in a wide sense, that is, systems which can be treated by analytical means. The present review offers a survey of such models starting the classical Friedrichs result and carrying further to recent developments in the theory of quantum graphs. Our attention concentrates on dynamical mechanism underlying resonance effects and at time evolution of the related unstable systems.