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.

Explains the connections between quantum chaos, quantum disorder, and cold atom physics in a unified framework Includes exercises and computational tasks for the reader, complete with hints and solutions Provides simple programs for numerical simulation and guidance for creating more complex or specialized routines The book emphasizes pedagogical care, making advanced topics accessible to graduate students and researchers

Autorentext

Jean-Claude Garreau received his PhD from the École Normale Supérieure in Paris in 1989 and joined CNRS in 1991, where he was a First Class Directeur de Recherche (senior researcher) when he retired in 2023. hHe started the Physics of Laser-Cooled Atoms Group (comprising seven permanent researchers) in the Physics Department of the Université de Lille, which developed an internationally-recognized expertise in quantum chaos and quantum disorder using the cold-atom realization of the paradigmatic system known as quantum kicked rotor as a quantum simulator.

Inhalt

Chapter 1: Classical Chaos.- Chapter 2: Quantum Chaos.- Chapter 3: Quantum Disorder.- Chapter 4: The Kicked Rotor.- Chapter 5: Manipulating Atoms With Light.