Nonlinearity and Chaos in Molecular Vibrations

1st Edition

Authors: Guozhen Wu
Hardcover ISBN: 9780444519061
eBook ISBN: 9780080459073
Imprint: Elsevier Science
Published Date: 30th June 2005
Page Count: 318
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Description

Nonlinearity and Chaos in Molecular Vibrations deals systematically with a Lie algebraic approach to the study of nonlinear properties of molecular highly excited vibrations. The fundamental concepts of nonlinear dynamics such as chaos, fractals, quasiperiodicity, resonance, and the Lyapunov exponent, and their roles in the study of molecular vibrations are presented.
The 20 chapters cover the basic ideas, the concept of dynamical groups, the integrable two-mode SU(2) system, the unintegrable three-mode SU(3) system, the noncompact su(1,1) algebraic application, su(3) symmetry breaking and its application and the quantal effect of asymmetric molecular rotation. Emphasis is given to: resonance and chaos, the fractal structure of eigencoefficients, the C-H bend motion of acetylene, regular and chaotic motion of DCN, the existence of approximately conserved quantum numbers, one-electronic motion in multi-sites, the Lyapunov exponent, actions of periodic trajectories and quantization, the H function and its application in vibrational relaxation as well as the Dixon dip and its destruction and chaos in the transitional states. This approach bridges the gap between molecular vibrational spectroscopy and nonlinear dynamics.
The book presents a framework of information that readers can use to build their knowledge, and is therefore highly recommended for all those working in or studying molecular physics, molecular spectroscopy, chemical physics and theoretical physics.

Key Features

  • Discusses nonlinearity and chaotic phenomena in molecular vibrations
  • Approaches the complicated highly excited molecular vibration
  • Provides clear information for students and researchers looking to expand knowledge in this field

Readership

Students and researchers in physics, chemistry and spectroscopy

Table of Contents

Chapter Headings

  1. Molecular vibration
  2. Concepts of dynamical groups
  3. Concepts in nonlinear dynamics
  4. Application of su(2) algebra
  5. Application of noncompact su(1,1) algebra
  6. Breaking of su(3) algebra and its application
  7. Application of su(3) algebra
  8. Quantal effect of asymmetric molecular rotation
  9. Pendulum, resonance and molecular highly excited vibration
  10. Quasiperiodicity, resonance overlap and chaos
  11. Fractal structure of eigencoefficients
  12. C-H bend motion of acetylene
  13. Lyapunov exponent and nonergodicity of C-H bend motion of acetylene
  14. Chaotic and periodic motions of DCN
  15. Regular classification of highly excited vibrational levels and its physical background
  16. One-electronic motion in multiple sites
  17. Lyapunov exponent, action integrals of periodic trajectories and quantization
  18. Application of the H function in vibrational relaxation
  19. The Dixon dip and its destruction
  20. Chaos in transitional states

Details

No. of pages:
318
Language:
English
Copyright:
© Elsevier Science 2005
Published:
Imprint:
Elsevier Science
eBook ISBN:
9780080459073
Hardcover ISBN:
9780444519061

About the Author

Guozhen Wu

Affiliations and Expertise

Department of Physics, Tsinghua University, Beijing, China

Reviews

Nonlinearity and Chaos in Molecular Vibrations deals systematically with a Lie algebraic approach to the study of nonlinear properties of molecular highly excited vibrations. The fundamental concepts of nonlinear dynamics such as chaos, fractals, quasiperiodicity, resonance, and the Lyapunov exponent, and their roles in the study of molecular vibrations are presented.
The 20 chapters cover the basic ideas, the concept of dynamical groups, the integrable two-mode SU(2) system, the unintegrable three-mode SU(3) system, the noncompact su(1,1) algebraic application, su(3) symmetry breaking and its application and the quantal effect of asymmetric molecular rotation. Emphasis is given to: resonance and chaos, the fractal structure of eigencoefficients, the C-H bend motion of acetylene, regular and chaotic motion of DCN, the existence of approximately conserved quantum numbers, one-electronic motion in multi-sites, the Lyapunov exponent, actions of periodic trajectories and quantization, the H function and its application in vibrational relaxation as well as the Dixon dip and its destruction and chaos in the transitional states. This approach bridges the gap between molecular vibrational spectroscopy and nonlinear dynamics.
The book presents a framework of information that readers can use to build their knowledge, and is therefore highly recommended for all those working in or studying molecular physics, molecular spectroscopy, chemical physics and theoretical physics.