Quantum decay and Friedrichs-Lee model

Prologue. Quantum dynamics is a vast and compelling subject with many mathematical and physical intricacies still awaiting for a thorough explanation. In this work we will study a generalization of a quantum mechanical system commonly known as Friedrichs-Lee model, frequently encountered in high-energy and atomic physics, which furnishes a description of a two-level system coupled with a structured bosonic bath; its dynamical features will be examined in some significant cases, showing that our model can exhibit both decaying and recurrent dynamics depending on the structure of the bath.
This dissertation is organized as follows: starting from a general discussion about the temporal behavior of quantum mechanical systems, with particular emphasis to the insurgence (or lack thereof) of exponential decay in quantum models, we will introduce the Friedrichs-Lee Hamiltonian and, after a detailed mathematical analysis of its features, we will be able to describe its temporal evolution and will analyze it in the light of the general discussion provided in the introductory chapter.