Skip to main content
  • Book
  • © 2003

Adiabatic Perturbation Theory in Quantum Dynamics

Authors:

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1821)

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

This is a preview of subscription content, access via your institution.

Table of contents (8 chapters)

  1. Front Matter

    Pages I-VI
  2. 1 Introduction

    • Stefan Teufel
    Pages 1-31
  3. 2 First order adiabatic theory

    • Stefan Teufel
    Pages 33-69
  4. 3 Space-adiabatic perturbation theory

    • Stefan Teufel
    Pages 71-104
  5. 4 Applications and extensions

    • Stefan Teufel
    Pages 105-140
  6. 5 Quantum dynamics in periodic media

    • Stefan Teufel
    Pages 141-171
  7. 6 Adiabatic decoupling without spectral gap

    • Stefan Teufel
    Pages 173-201
  8. Appendix

    • Stefan Teufel
    Pages 203-224
  9. List of symbols and References

    • Stefan Teufel
    Pages 225-234
  10. Back Matter

    Pages 235-236

About this book

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.

Keywords

  • Pseudodifferential Operators
  • Quantum mechanics
  • adiabatic limit
  • calculus
  • equation
  • semiclassical limit
  • partial differential equations

Reviews

From the reviews:

"The present monograph is devoted to a generalizing approach to adiabatic theory developed in recent years … . The book is clearly structured. The introduction gives an excellent non-technical overview of the problems and ideas involved. … this very readable book is a valuable reference for researchers in mathematical physics." (Karl Michael Schmidt, Mathematical Reviews, Issue 2006 g)

Bibliographic Information

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions