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The Geometric Phase in Quantum Systems

Foundations, Mathematical Concepts, and Applications in Molecular and Condensed Matter Physics

  • Arno Bohm
  • Ali Mostafazadeh
  • Hiroyasu Koizumi
  • Qian Niu
  • Joseph Zwanziger

Part of the Texts and Monographs in Physics book series (TMP)

Table of contents

  1. Front Matter
    Pages I-XVII
  2. Arno Bohm, Ali Mostafazadeh, Hiroyasu Koizumi, Qian Niu, Joseph Zwanziger
    Pages 1-4
  3. Arno Bohm, Ali Mostafazadeh, Hiroyasu Koizumi, Qian Niu, Joseph Zwanziger
    Pages 5-30
  4. Arno Bohm, Ali Mostafazadeh, Hiroyasu Koizumi, Qian Niu, Joseph Zwanziger
    Pages 31-52
  5. Arno Bohm, Ali Mostafazadeh, Hiroyasu Koizumi, Qian Niu, Joseph Zwanziger
    Pages 53-64
  6. Arno Bohm, Ali Mostafazadeh, Hiroyasu Koizumi, Qian Niu, Joseph Zwanziger
    Pages 65-105
  7. Arno Bohm, Ali Mostafazadeh, Hiroyasu Koizumi, Qian Niu, Joseph Zwanziger
    Pages 107-127
  8. Arno Bohm, Ali Mostafazadeh, Hiroyasu Koizumi, Qian Niu, Joseph Zwanziger
    Pages 129-145
  9. Arno Bohm, Ali Mostafazadeh, Hiroyasu Koizumi, Qian Niu, Joseph Zwanziger
    Pages 147-193
  10. Arno Bohm, Ali Mostafazadeh, Hiroyasu Koizumi, Qian Niu, Joseph Zwanziger
    Pages 195-224
  11. Arno Bohm, Ali Mostafazadeh, Hiroyasu Koizumi, Qian Niu, Joseph Zwanziger
    Pages 225-253
  12. Arno Bohm, Ali Mostafazadeh, Hiroyasu Koizumi, Qian Niu, Joseph Zwanziger
    Pages 255-275
  13. Arno Bohm, Ali Mostafazadeh, Hiroyasu Koizumi, Qian Niu, Joseph Zwanziger
    Pages 277-299
  14. Arno Bohm, Ali Mostafazadeh, Hiroyasu Koizumi, Qian Niu, Joseph Zwanziger
    Pages 301-336
  15. Arno Bohm, Ali Mostafazadeh, Hiroyasu Koizumi, Qian Niu, Joseph Zwanziger
    Pages 337-359
  16. Arno Bohm, Ali Mostafazadeh, Hiroyasu Koizumi, Qian Niu, Joseph Zwanziger
    Pages 361-405
  17. Arno Bohm, Ali Mostafazadeh, Hiroyasu Koizumi, Qian Niu, Joseph Zwanziger
    Pages 407-427
  18. Back Matter
    Pages 429-443

About this book

Introduction

Aimed at graduate physics and chemistry students, this is the first comprehensive monograph covering the concept of the geometric phase in quantum physics from its mathematical foundations to its physical applications and experimental manifestations. It contains all the premises of the adiabatic Berry phase as well as the exact Anandan-Aharonov phase. It discusses quantum systems in a classical time-independent environment (time dependent Hamiltonians) and quantum systems in a changing environment (gauge theory of molecular physics). The mathematical methods used are a combination of differential geometry and the theory of linear operators in Hilbert Space. As a result, the monograph demonstrates how non-trivial gauge theories naturally arise and how the consequences can be experimentally observed. Readers benefit by gaining a deep understanding of the long-ignored gauge theoretic effects of quantum mechanics and how to measure them.

Keywords

Aharanov-Bohm Effect Berry Phase Gauge theory Geometric Phase Hall Effect Helium-Atom-Streuung Jahn-Teller System Potential REM Spin Systems Topological Phase mathematical physics molecule quantum mechanics quantum system

Authors and affiliations

  • Arno Bohm
    • 1
  • Ali Mostafazadeh
    • 2
  • Hiroyasu Koizumi
    • 3
  • Qian Niu
    • 1
  • Joseph Zwanziger
    • 4
  1. 1.Physics DepartmentUniversity of Texas at AustinAustinUSA
  2. 2.Department of MathematicsKoç UniversityIstanbulTurkey
  3. 3.Faculty of ScienceHimeji Institute of TechnologyHyogoJapan
  4. 4.Department of ChemistryIndiana UniversityBloomingtonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-10333-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 2003
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-05504-1
  • Online ISBN 978-3-662-10333-3
  • Series Print ISSN 1864-5879
  • Series Online ISSN 1864-5887
  • Buy this book on publisher's site
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