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

• Published in: Entropy (Basel, Switzerland) Vol. 25; no. 3; p. 423
• Main Authors: Bountis, Tassos, Macías-Díaz, Jorge E
• Format: Journal Article
• Language: English
• Published: Switzerland MDPI AG 26.02.2023; MDPI
• Subjects: Amplitudes; Analysis; Eigenvalues; Forbidden bands; Hamiltonian lattices; Hamiltonian systems; Investigations; Lattice theory; Lattice vibration; Lattices; Mathematical models; Mathematical research; on-site potential; Onsite; Perturbation; supratransmission; system with long-range interactions; Thresholds; Greece; supratransmission; on-site potential; system with long-range interactions; Hamiltonian lattices
• ISSN: 1099-4300; 1099-4300
• DOI: 10.3390/e25030423

We investigated a class of one-dimensional (1D) Hamiltonian -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<α<∞ and 0<β<∞, as the effect of the on-site potential terms of the Hamiltonian varied. In previous works, we studied the critical amplitude As(α,Ω) at which supratransmission occurs, for one range parameter α, 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 As(α,Ω) increases monotonically the longer the range of interactions is (i.e., as α⟶0). However, when on-site potential terms are taken into account, As(α,Ω) reaches a maximum at a low value of α that depends on Ω, below which supratransmission thresholds 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.