量子混沌导论（英文版）

    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 prin-ciples 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. A basic knowledge of quantum mechanics is assumed.

    H-J Stockmann was born in 1945 in Gottingen, Germany. He started his studies in physics and mathematics in 1964 at the University of Heidelberg. He performed his diploma work in experimental physics, on Optical spectroscopy which the finished in 1969. For his doctoral work he changed to nuclear solid state physics, with experiments at the research reactor of the Kernforschungszentrum karlsruhe.

Preface
1 Introduction
2 Billiard experiments
　2.1 Wave propagation in solids and liquids
　　2.1.1 Chladni figures
　　2.1.2 Water surface waves
　　2.1.3 Vibrating blocks
　　2.1.4 Ultrasonic fields in water-filled cavities
　2.2 Microwave billiards
　　2.2.1 Basic principles
　　2.2.2 Field distributions in microwave cavities
　　2.2.3 Billiards with broken time-reversal symmetry
　　2.2.4 Josephsonjunctions
　2.3 Mesoscopic structures
　　2.3.1 Antidot lattices
　　2.3.2 Quantum dot billiards
　　2.3.3 Quantum well billiards
　　2.3.4 Quantum corrals
3 Random matrices
　3.1 Gaussian ensembles
3.1.1 Symmetries
3.1.2 Univeraslity classes
3.1.3 Definition of the Gaussian ensembles
3.1.4 Correlated eigenenergy distribution
3.1.5 Averaged density of states
3.2 Spectral correlations
……
3.3 Supersymmetry method
4 Floquet and tight-binding systems
4.1 Hamiltonians with periodic time depedences
4.2 Dynamical localization
4.3 Tight-binding systems
5 Eigenvalue dynamics
5.1 Pechukas-Yukawa model
5.2 Billiard level dynamics
5.3 Geometrical phases
6 Scattering systems
6.1 Billiards as scattering systems
6.2 Amplitude distribution functions
6.3 Fluctuation properties of the scattering matrix
7 Semiclassical quantum mechanics
7.1 Integrable systems
7.2 Gutzwiller trace formula
7.3 Contributions to the density of states
8 Applications of periodic orbit theory
8.1 Periodic orbit analysis of spectra and wave functions
8.2 Semiclassical theory of spectral rigidity
8.3 Periodic orbit calculation of spectra
8.4 Surfaces with constant negative curvature
References
Index

This monograph is based on the script of a lecture series on the quantum mechanics of classically chaotic systems given by the author at the University of Marburg during the summer term 1995. The lectures were attended by students with basic knowledge in quantum mechanics, including members of the author's own group working on microwave analogous experiments on quantum chaotic questions. . When preparing the lectures the author became aware that a comprehensive textbook, covering both the theoretical and the experimental aspects, was not av..