160 pages, 9x6 inches
March 2001 Hardcover
ISBN 1-58949-001-0


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This book, for the first time, presents a review on transition from regular dynamics to quantum chaos in a quantum degenerate system -- a harmonic oscillator perturbed by a monochromatic wave. The model, being one of the simplest dynamical systems, exhibits the fundamental properties of nonlinearity, quantum instability and chaos. And, more importantly, it describes practical systems such as an ion in a linear ion trap interacting with laser radiation, an electron in magnetic field interacting with a plasma wave, an acoustic quantum cyclotron resonance in metals, and a two-dimensional electron gas in semiconductor heterostructures. This book explains in details how the transition to quantum chaos occurs and how the theoretical predictions can be tested in experiments. The book is useful to students and scientists who are interested to understand the nature of quantum instabilities and chaos in dynamic systems and their applications in technological problems.


Ch.1 Introduction
Ch.2 Classical Resonance Perturbation Theory
Ch.3 Stability of the Classical Ground State 
Ch.4 Dynamics of an Ion in a Linear Ion Trap 
Ch.5 Quantum Resonance Cells
Ch.6 Symmetry of the Quasienergy States
Ch.7 Tunneling Between Resonance Cells
Ch.8 Weak Quantum Chaos
Ch.9 Quantum Chaos of an Ion in a Linear Trap
Ch.10 Dynamics of the Monochromatically Perturbed Oscillator as a Solid-state Problem of Electron Localization
Ch.11 Stability of the Quantum Ground State
Ch.12 Conclusion 

Dr. Dmitry I. Kamenev is a specialist in classical and quantum chaos in dynamical systems. He is currently a guest scientist in the Theoretical Division and Center for Nonlinear Studies at the Los Alamos National Laboratory. 

Dr. Gennady P. Berman, a staff member of the Theoretical Division at the Los Alamos National Laboratory, is an expert in classical and quantum dynamical systems, dynamical chaos and applications to magnetic and mesoscopic systems, quantum optics and quantum computation. He has published over 150 research papers on classical and quantum dynamical systems, nanotechnology, and dynamics of quantum computation and other areas. He is a co-author of the books Introduction to Quantum Computers (1998), Crossover-time in Quantum Boson and Spin Systems (1994), and Introduction to Quantum Neural Technologies (2002).