Chapter 20. Slow Relaxation in Hamiltonian Systems with Internal Degrees of Freedom

  1. M. Toda3,
  2. T. Komatsuzaki4,
  3. T. Konishi5,
  4. R. S. Berry6 and
  5. S. A. Rice7
  1. Akira Shudo1 and
  2. Shinji Saito2

Published Online: 27 JAN 2005

DOI: 10.1002/0471712531.ch20

Geometric Structures of Phase Space in Multidimensional Chaos: Applications to Chemical Reaction Dynamics in Complex Systems, Volume 130

Geometric Structures of Phase Space in Multidimensional Chaos: Applications to Chemical Reaction Dynamics in Complex Systems, Volume 130

How to Cite

Shudo, A. and Saito, S. (2005) Slow Relaxation in Hamiltonian Systems with Internal Degrees of Freedom, in Geometric Structures of Phase Space in Multidimensional Chaos: Applications to Chemical Reaction Dynamics in Complex Systems, Volume 130 (eds M. Toda, T. Komatsuzaki, T. Konishi, R. S. Berry and S. A. Rice), John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471712531.ch20

Editor Information

  1. 3

    Physics Department, Nara Women's University, Nara, 630-8506, Japan

  2. 4

    Nonlinear Science Laboratory, Department of Earth and Planetary Sciences, Faculty of Science, Kobe University, Nada, Kobe, 657-8501, Japan

  3. 5

    Department of Physics, Nagoya University, Nagoya, 464-8602, Japan

  4. 6

    Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, USA

  5. 7

    Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 USA

Author Information

  1. 1

    Department of Physics, Tokyo Metropolitan University, Minami-Ohsawa, Hachioji, Tokyo, 192-0397, Japan

  2. 2

    Department of Chemistry, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8602, Japan

Publication History

  1. Published Online: 27 JAN 2005
  2. Published Print: 21 JAN 2005

Book Series:

  1. Advances in Chemical Physics

Book Series Editors:

  1. Stuart A. Rice

Series Editor Information

  1. Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 USA

ISBN Information

Print ISBN: 9780471711582

Online ISBN: 9780471712534

SEARCH

Keywords:

  • slow relaxation;
  • liquid water;
  • molecular dynamical simulation;
  • phase space bottleneck;
  • internal degrees of freedom;
  • Boltzmann–Jeans conjecture;
  • Nekhoroshev theory;
  • potential landscape picture

Summary

We examine origins of slow relaxation observed in Molecular dynamics simulations of liquids in the light of the theory of Hamiltonian systems. Perturbation theories as well as several scenarios creating bottlenecks in multi-dimensional phase space are reviewed and criticized as a possible candidate which explains especially intermittent behaviors found in liquid water at room temperatures. We propose that the presence of internal degrees of freedom is a crucial ingredient to ensure slow relaxations in large dimensional molecular systems. The mechanism is reminiscent of the so-called Boltzmann–Jeans conjecture which admits a modern interpretation based on Nekhoroshev-type theory of Hamiltonian systems. We discuss the relation between the potential energy landscape picture and the picture thus proposed.