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Title: Lyapunov instability versus relaxation time in two coupled oscillators

Abstract

We consider the relation between relaxation time and the largest Lyapunov exponent in a system of two coupled oscillators, one of them being harmonic. It has been found that in a rather broad region of parameter space, contrary to the common expectation, both Lyapunov exponent and relaxation time increase as a function of the total energy. This effect is attributed to the fact that above a critical value of the total energy, although the Lyapunov exponent increases, Kolmogorov-Arnold-Moser tori appear and the chaotic fraction of phase space decreases. We examine the required conditions and demonstrate the key role of the dispersion relation for this behavior to occur. This study is useful, among other things, in the understanding of the damping of nuclear giant resonances.

Authors:
; ;  [1];  [2];  [3];  [4]
  1. Department of Physics, University of Athens, GR-15771, Athens (Greece)
  2. Institute of Microelectronics (IMEL), NCSR 'Demokritos', P. O. Box 60228, Aghia Paraskevi, Attiki, 15310 (Greece)
  3. (Greece)
  4. Institut fuer Kernphysik, Technische Universitaet Darmstadt, Schlossgartenstr. 9, D-64289 Darmstadt (Germany)
Publication Date:
OSTI Identifier:
21069755
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; Journal Volume: 73; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevE.73.016204; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHAOS THEORY; DAMPING; DISPERSION RELATIONS; GIANT RESONANCE; INSTABILITY; LYAPUNOV METHOD; OSCILLATORS; PHASE SPACE; RELAXATION TIME; TORI

Citation Formats

Papachristou, P. K., Mavrommatis, E., Diakonos, F. K., Constantoudis, V., Physics Department, National Technical University, Athens, and Wambach, J. Lyapunov instability versus relaxation time in two coupled oscillators. United States: N. p., 2006. Web. doi:10.1103/PHYSREVE.73.016204.
Papachristou, P. K., Mavrommatis, E., Diakonos, F. K., Constantoudis, V., Physics Department, National Technical University, Athens, & Wambach, J. Lyapunov instability versus relaxation time in two coupled oscillators. United States. doi:10.1103/PHYSREVE.73.016204.
Papachristou, P. K., Mavrommatis, E., Diakonos, F. K., Constantoudis, V., Physics Department, National Technical University, Athens, and Wambach, J. Sun . "Lyapunov instability versus relaxation time in two coupled oscillators". United States. doi:10.1103/PHYSREVE.73.016204.
@article{osti_21069755,
title = {Lyapunov instability versus relaxation time in two coupled oscillators},
author = {Papachristou, P. K. and Mavrommatis, E. and Diakonos, F. K. and Constantoudis, V. and Physics Department, National Technical University, Athens and Wambach, J.},
abstractNote = {We consider the relation between relaxation time and the largest Lyapunov exponent in a system of two coupled oscillators, one of them being harmonic. It has been found that in a rather broad region of parameter space, contrary to the common expectation, both Lyapunov exponent and relaxation time increase as a function of the total energy. This effect is attributed to the fact that above a critical value of the total energy, although the Lyapunov exponent increases, Kolmogorov-Arnold-Moser tori appear and the chaotic fraction of phase space decreases. We examine the required conditions and demonstrate the key role of the dispersion relation for this behavior to occur. This study is useful, among other things, in the understanding of the damping of nuclear giant resonances.},
doi = {10.1103/PHYSREVE.73.016204},
journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},
number = 1,
volume = 73,
place = {United States},
year = {Sun Jan 15 00:00:00 EST 2006},
month = {Sun Jan 15 00:00:00 EST 2006}
}