Slow relaxation in heterogeneous Hamiltonian systems: Numerical study compared with Landau-Teller approximation

Yoshihiro Watanabe, Nobuko Fuchikami

Research output: Contribution to journalArticle

Abstract

We performed numerical simulations on a one-dimensional diatomic gas to investigate the possible long time scale in Hamiltonian systems with internal degrees of freedom. In the limit of the large system size, the time scale for energy sharing between the translational motion and the vibrational one grows as ∼ exp [B ωα] with the vibrational frequency ω where 0 < α < 1. Although the present results agree fairly well with the Landau-Teller approximation in which α = 0.4, we note a slight deviation of an optimized α from this value. We ascribe it to a non-Debye type dynamics by presenting 1 / fβ like spectra of energy fluctuations. The simulations show that the complete resonance condition for vibrational frequencies assumed in the analytical treatment is not essential for the long time scale.

Original languageEnglish
Pages (from-to)315-328
Number of pages14
JournalPhysica A: Statistical Mechanics and its Applications
Volume378
Issue number2
DOIs
Publication statusPublished - May 15 2007

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Heterogeneous Systems
Hamiltonian Systems
Numerical Study
Time Scales
Approximation
approximation
diatomic gases
translational motion
Energy
Sharing
Deviation
simulation
degrees of freedom
Degree of freedom
Fluctuations
Internal
deviation
Numerical Simulation
Motion
energy

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Condensed Matter Physics

Cite this

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abstract = "We performed numerical simulations on a one-dimensional diatomic gas to investigate the possible long time scale in Hamiltonian systems with internal degrees of freedom. In the limit of the large system size, the time scale for energy sharing between the translational motion and the vibrational one grows as ∼ exp [B ωα] with the vibrational frequency ω where 0 < α < 1. Although the present results agree fairly well with the Landau-Teller approximation in which α = 0.4, we note a slight deviation of an optimized α from this value. We ascribe it to a non-Debye type dynamics by presenting 1 / fβ like spectra of energy fluctuations. The simulations show that the complete resonance condition for vibrational frequencies assumed in the analytical treatment is not essential for the long time scale.",
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AB - We performed numerical simulations on a one-dimensional diatomic gas to investigate the possible long time scale in Hamiltonian systems with internal degrees of freedom. In the limit of the large system size, the time scale for energy sharing between the translational motion and the vibrational one grows as ∼ exp [B ωα] with the vibrational frequency ω where 0 < α < 1. Although the present results agree fairly well with the Landau-Teller approximation in which α = 0.4, we note a slight deviation of an optimized α from this value. We ascribe it to a non-Debye type dynamics by presenting 1 / fβ like spectra of energy fluctuations. The simulations show that the complete resonance condition for vibrational frequencies assumed in the analytical treatment is not essential for the long time scale.

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