Chapter 9. Coarse-Grained Picture for Controlling Quantum Chaos

  1. M. Toda5,
  2. T. Komatsuzaki6,
  3. T. Konishi7,
  4. R. S. Berry8 and
  5. S. A. Rice9
  1. Toshiya Takami1,†,
  2. Hiroshi Fujisaki2 and
  3. Takayuki Miyadera3

Published Online: 27 JAN 2005

DOI: 10.1002/0471712531.ch9

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

Takami, T., Fujisaki, H. and Miyadera, T. (2005) Coarse-Grained Picture for Controlling Quantum Chaos, 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.ch9

Editor Information

  1. 5

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

  2. 6

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

  3. 7

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

  4. 8

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

  5. 9

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

Author Information

  1. 1

    Institute for Molecular Science, Okazaki, 444-8585, Japan

  2. 2

    Department of Chemistry, Boston University, Boston, Massachusetts, 02215, USA

  3. 3

    Department of Information Sciences, Tokyo University of Science, Noda City, 278-8510, Japan

  1. Computing and Communications Center, Kyushu University, Fukuoka, 812-8581, 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:

  • Rabi frequency;
  • optimal control theory;
  • random matrix;
  • kicked rotor;
  • quantum chaos;
  • coarse grain

Summary

We propose a coarse-grained picture to analyze control problems for quantum chaos systems. Using optimal control theory, we first show that almost perfect control is achieved for random matrix systems and a quantum kicked rotor. Second, under the assumption that the controlled dynamics is well described by a Rabi-type oscillation between unperturbed states, we derive an analytic expression for the optimal field. Finally we numerically confirm that the analytic field can steer an initial state to a target state in random matrix systems.