Quantum Chaos. An Introduction

This book introduces the quantum mechanics of classically chaotic systems, or Quantum Chaos for short. The basic concepts of quantum chaos can be grasped easily by any student of physics, but the underlying physical principles tend to be obscured by the mathematical apparatus used to describe it. The author's philosophy, therefore, has been to keep the discussion simple and to illustrate theory, wherever possible, with experimental or numerical examples. The microwave billiard experiments, initiated by the author and his group, play a major role in this respect. The author assumes a basic knowledge of quantum mechanics. Beginning with a presentation of the various types of billiard experiment, random matrix theory is described, including an introduction to supersymmetry techniques. There is a chapter that deals with systems with periodic time dependences, with special emphasis on dynamical localization. Another topic is the analogy between the dynamics of a one-dimensional gas with a repulsive interaction and spectral level dynamics, where an external parameter takes the role of time. In another chapter on scattering theory distributions and fluctuations, properties of scattering matrix elements are presented. In the final two chapters semiclassical quantum mechanics and periodic orbit theory are addressed, including a derivation of the Gutzwiller trace formula together with a number of applications. This book will be of great value to anyone working in quantum chaos.