The Effect of On-Site Potentials on Supratransmission in One-Dimensional Hamiltonian Lattices

We investigated a class of one-dimensional (1D) Hamiltonian N-particle lattices whose binary interactions are quadratic and/or quartic in the potential. We also included on-site potential terms, frequently considered in connection with localization phenomena, in this class. Applying a sinusoidal perturbation at one end of the lattice and an absorbing boundary on the other, we studied the phenomenon of supratransmission and its dependence on two ranges of interactions, [Formula: see text] and [Formula: see text] , as the effect of the on-site potential terms of the Hamiltonian varied. In previous works, we studied the critical amplitude [Formula: see text] at which supratransmission occurs, for one range parameter [Formula: see text] , and showed that there was a sharp threshold above which energy was transmitted in the form of large-amplitude nonlinear modes, as long as the driving frequency [Formula: see text] lay in the forbidden band-gap of the system. In the absence of on-site potentials, it is known that [Formula: see text] increases monotonically the longer the range of interactions is (i.e., as [Formula: see text]). However, when on-site potential terms are taken into account, [Formula: see text] reaches a maximum at a low value of [Formula: see text] that depends on [Formula: see text] , below which supratransmission thresholds decrease sharply to lower values. In this work, we studied this phenomenon further, as the contribution of the on-site potential terms varied, and we explored in detail their effect on the supratransmission thresholds.