Read our Editor's Choice Article "The Effect of On-Site Potentials on Supratransmission in One-Dimensional Hamiltonian Lattices"

Authors: Tassos Bountis and Jorge E. Macías-Díaz

Abstract: 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, 0<??<∞ and 0<??<∞, as the effect of the on-site potential terms of the Hamiltonian varied. In previous works, we studied the critical amplitude ????(??,Ω) at which supratransmission occurs, for one range parameter ??, 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 Ω lay in the forbidden band-gap of the system. In the absence of on-site potentials, it is known that ????(??,Ω) increases monotonically the longer the range of interactions is (i.e., as ???0). However, when on-site potential terms are taken into account, ????(??,Ω) reaches a maximum at a low value of ?? that depends on Ω, 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.

Read full article at: mdpi.com/1099-4300/25/3/423

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