Longest Relaxation Time of Relaxation Processes for Classical and Quantum Brownian Motion in a Potential: Escape Rate Theory Approach

  1. Stuart A. Rice and
  2. Aaron R. Dinner
  1. William T. Coffey1,
  2. Yuri P. Kalmykov2,
  3. Serguey V. Titov3 and
  4. William J. Dowling1

Published Online: 27 MAR 2013

DOI: 10.1002/9781118571767.ch3

Advances in Chemical Physics, Volume 153

Advances in Chemical Physics, Volume 153

How to Cite

Coffey, W. T., Kalmykov, Y. P., Titov, S. V. and Dowling, W. J. (2013) Longest Relaxation Time of Relaxation Processes for Classical and Quantum Brownian Motion in a Potential: Escape Rate Theory Approach, in Advances in Chemical Physics, Volume 153 (eds S. A. Rice and A. R. Dinner), John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118571767.ch3

Editor Information

  1. Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois, USA

Author Information

  1. 1

    Department of Electronic and Electrical Engineering, Trinity College, Dublin 2, Ireland

  2. 2

    Laboratoire de Mathématiques et Physique, Université de Perpignan Via Domitia, 52 Avenue Paul Alduy, 66860 Perpignan Cedex, France

  3. 3

    Kotelnikov Institute of Radio Engineering and Electronics of the Russian Academy of Sciences, Vvedenskii Square 1, Fryazino, Moscow Region 141190, Russian Federation

Publication History

  1. Published Online: 27 MAR 2013
  2. Published Print: 19 APR 2013

ISBN Information

Print ISBN: 9781118477861

Online ISBN: 9781118571767

SEARCH

Keywords:

  • quantum Brownian in a potential;
  • classical Brownian and escape rate;
  • Brownian, longest relaxation time;
  • Kramers turnover/Langer's for IHD;
  • Fokker–Planck, quasianalytical

Summary

This chapter contains sections titled:

  • Introduction

  • Escape Rate for Classical Brownian Motion

  • Quantum Brownian Motion in a Potential

  • Conclusion

  • Acknowledgment

  • Appendix A: Wiener–Hopf Method

  • Appendix B: Matrices and Vectors Involved in the Matrix Continued Fraction Solutions

  • Appendix C: Evaluation of Averages in the Undamped Limit

  • Appendix D: Escape Rate in the IHD Limit

  • Appendix E: Justification of Semiclassical Representation of Matrix Elements

  • References