Energy Transports in Toda Lattices with Quasiperiodic On-site Potentials

Abstract

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 ѓ for different nonlinear parameters Į and different strengths of on-site potentials į. In the thermodynamic limit, the dependence of T eq on ѓ is found to display a power law behaviour, that is,The exponenet a is found to be -2.03 and is independent of the values of Į and į.