Chapter 8. Classical Mechanism of Multidimensional Barrier Tunneling

  1. M. Toda3,
  2. T. Komatsuzaki4,
  3. T. Konishi5,
  4. R. S. Berry6 and
  5. S. A. Rice7
  1. Kin'ya Takahashi1 and
  2. Kensuke S. Ikeda2

Published Online: 27 JAN 2005

DOI: 10.1002/0471712531.ch8

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

Takahashi, K. and Ikeda, K. S. (2005) Classical Mechanism of Multidimensional Barrier Tunneling, 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.ch8

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

    The Physics Laboratories, Kyushu Institute of Technology, Iizuka, 820-8502, Japan

  2. 2

    Department of Physical Sciences, Faculty of Science and Engineering, Ritsumeikan University, Kusatsu, 525-8577, 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

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Keywords:

  • multi-dimensional tunneling;
  • complex semiclassical method;
  • fringed tunneling;
  • heteroclinic-like entanglement;
  • movable singularities

Summary

Multi-dimensionality of systems significantly affects on tunneling phenomena observed. In particular, if a system under consideration is classically non-integrable, very complicated tunneling phenomena, so called chaotic tunneling, are observed. The aim of this short review is to explain the underlying classical mechanism of multi-dimensional barrier tunneling by using the semiclassical method based on classical dynamics extended to the complex domain, i.e., complex semiclassical method. The tunneling probability of multi-dimensional barrier systems is still well reproduced by using the complex semiclassical method even in the chaotic tunneling regime, in which a characteristic tunneling phenomenon, i.e. the fringed tunneling, is observed. However the classical trajectories guided by complexified stable and unstable manifold dominantly contribute to the tunneling probability, which gives quite a different picture of the tunneling from that given by the ordinary instanton mechanism.