Energy localization in the Φ4 oscillator chain
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2006-05-29
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We study energy localization in a finite one-dimensional Φ4 oscillator chain with initial energy in a single oscillator of the chain. We numerically calculate the effective number of degrees of freedom sharing the energy on the lattice as a function of time. We find that for energies smaller than a critical value, energy equipartition among the oscillators is reached in a relatively short time. On the other hand, above the critical energy, a decreasing number of particles sharing the energy is observed. We give an estimate of the effective number of degrees of freedom as a function of the energy. Our results suggest that localization is due to the appearance, above threshold, of a breather-like structure. Analytic arguments are given, based on the averaging theory and the analysis of a discrete nonlinear Schrödinger equation approximating the dynamics, to support and explain the numerical results. © 2006 The American Physical Society.
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Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, v. 73, n. 5, 2006.