Quantum Chaos and Disorder: An Introduction with Sample Programs and Exercises

This textbook on quantum chaos, quantum disorder, and connections to modern atomic and condensed matter physics is accessible to advanced undergraduate and graduate students, but will also be a useful reference for researchers. As well as presenting a unique set of topics, the goal of the book is to develop physical intuition, but unlike other texts on quantum chaos, the reader is invited to explore the subject via a selection of numerical simulations tasks. To achieve this goal, the book introduces and discusses subjects like quantum chaos, quantum disorder, random matrix theory, and the Anderson model, illustrating them with the quantum kicked rotor (QKR). The kicked rotor, a paradigmatic system for both quantum chaos and quantum disorder, is conceptually very simple but many interesting aspects of its dynamics (both quantum and classical) can be easily simulated. A chapter on ultracold atoms allows the reader to understand the experimental realization of the QKR using only Masters-level quantum mechanics and also covers a variety of aspects ranging from Bose-Einstein condensates to quantum simulators. The final part of the chapter is dedicated to the timely subject of interparticle interactions which lead to novel phenomena like many-body localization in disordered systems and quasi-classical chaos in quantum systems, opening a window to current research topics. Some simple programs are provided in standard languages like Python or C]+ and using shared routine packs like FFTW3 and Eigen, along with guidance for readers to write their own routines to explore more specialized or advanced scenarios. The chapters are largely self-contained, and each one is furnished with exercises and computational tasks along with selected solutions and hints, making the book ideal for a taught course on its main theme or as supplementary reading for advanced condensed matter and quantum physics courses. An apendix provides background material to help the readers who need some complementary instruction in specific points, and another apendix introduces the most useful numerical methods.