Abstract
We study numerically the process of energy transports in Toda lattices with quasiperiodic on-site potentials. The total energy was initially equidistributed the 10% of lowest frequency linear modes. For Toda model without on-site potentials, only several new low frequency modes are excited, but the energy equipartition is not achieved. When the quasiperiodic on-site potentials are added, the energy transfers continuously to the high frequency modes and finally evolves towards energy equipartition. We further study the equipartition time T eq as a function of energy density e for different nonlinear parameters α and different strengths of on-site potentials δ. In the thermodynamic limit, the dependence of T eq on e is found to display a power law behaviour, that is, T eq ∝ e a . The exponenet a is found to be -2.03 and is independent of the values of α and δ.
Highlights
The study of energy transfers in nonlinear lattices has a long history but is still far from been completed
We study the equipartition time Teq as a function of energy density ѓ for different nonlinear parameters Į and different strengths of on-site potentials į
For fixed ܭ, it is found that more time is required to approach energy equipartition when Į is decreased
Summary
The study of energy transfers in nonlinear lattices has a long history but is still far from been completed. In a relative short time scale, a kind of metastable state is appeared In this state, in addition to the initial excited states, only several new low frequency modes are excited, but still far from energy equipartition. In addition to the initial excited states, only several new low frequency modes are excited, but still far from energy equipartition This is the state observed in the original FPU paper [1]. We are devoted to the energy transport problem in Toda model with the effect of quasiperiodic on-site potentials. Whether can the energy equipartition being achieved with the effect of quasiperiodic on-site potentials If it dose, what is the scaling law for the equipartition time Teq as a function of the energy density ܭin the thermodynamic limit.
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