Adiabatic Perturbation Theory in Quantum Dynamics

✍ Scribed by Stefan Teufel (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2003
• Tongue: English
• Leaves: 238
• Series: Lecture Notes in Mathematics 1821
• Edition: 1
• Category: Library

✦ Synopsis

Separation of scales plays a fundamental role in the understanding of the dynamical behaviour of complex systems in physics and other natural sciences. A prominent example is the Born-Oppenheimer approximation in molecular dynamics. This book focuses on a recent approach to adiabatic perturbation theory, which emphasizes the role of effective equations of motion and the separation of the adiabatic limit from the semiclassical limit.

A detailed introduction gives an overview of the subject and makes the later chapters accessible also to readers less familiar with the material. Although the general mathematical theory based on pseudodifferential calculus is presented in detail, there is an emphasis on concrete and relevant examples from physics. Applications range from molecular dynamics to the dynamics of electrons in a crystal and from the quantum mechanics of partially confined systems to Dirac particles and nonrelativistic QED.

✦ Table of Contents

1 Introduction....Pages 1-31
2 First order adiabatic theory....Pages 33-69
3 Space-adiabatic perturbation theory....Pages 71-104
4 Applications and extensions....Pages 105-140
5 Quantum dynamics in periodic media....Pages 141-171
6 Adiabatic decoupling without spectral gap....Pages 173-201
Appendix....Pages 203-224
List of symbols and References....Pages 225-234

✦ Subjects

Theoretical, Mathematical and Computational Physics; Operator Theory; Partial Differential Equations