Quantum Chaos An Introduction [Paperback]

Discusses quantum chaos, an important area of nonlinear science.In classically chaotic systems the evolution of the system is extremely sensitively dependent on initial conditions. Two trajectories starting with slightly different directions will behave completely differently after even just a short time. In quantum mechanics it is no longer possible to define a trajectory. Nevertheless, the fingerprints of classical chaos must be present in quantum mechanics, since in the semiclassical limit quantum mechanics turns into classical mechanics. Quantum chaos research looks for these fingerprints and studies in particular the relations between classical and quantum mechanics in the transition region.In classically chaotic systems the evolution of the system is extremely sensitively dependent on initial conditions. Two trajectories starting with slightly different directions will behave completely differently after even just a short time. In quantum mechanics it is no longer possible to define a trajectory. Nevertheless, the fingerprints of classical chaos must be present in quantum mechanics, since in the semiclassical limit quantum mechanics turns into classical mechanics. Quantum chaos research looks for these fingerprints and studies in particular the relations between classical and quantum mechanics in the transition region.This volume provides a comprehensive and highly accessible introduction to quantum chaos. It emphasizes both the experimental and theoretical aspects of quantum chaos, and includes a discussion of supersymmetry techniques. Theoretical concepts are developed clearly and illustrated by numerous experimental or numerical examples. The author also shares the first-hand insights that he gleaned from his initiation of the microwave billiard experiments. Additional topics covered include the random matrix theory, systems with periodic time dependences, the analogy between the dynamics of a one-dimensional gas with a repulsive interaction and spectrallCb