Energy transfer in the Holstein approach for the interplay between periodic on-site and linear acoustic potentials

• Published in: Wave motion Vol. 130; p. 103382
• Main Authors: Reza-Mejía, Sergio, Cisneros-Ake, Luis A.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.10.2024
• Subjects: Linear Schrödinger–sine-Gordon system; Pseudo-spectral solutions; Variational approach; Pseudo-spectral solutions; Linear Schrödinger–sine-Gordon system; Variational approach
• ISSN: 0165-2125
• DOI: 10.1016/j.wavemoti.2024.103382

We study the problem of a transferring electron along a lattice of phonons, in the continuous long wave limit, holding periodic on-site and linear longitudinal interactions in Holstein’s approach. We thus find that the continuum limit of our modeling produces an effective coupling between the linear Schrödinger and sine–Gordon equations. Then, we take advantage of the existence of trapped kink–anti kink solutions in the sine–Gordon equation to variationally describe traveling localized coupled solutions. We validate our variational findings by solving numerically the full coupled system. Very reasonable agreement is found between the variational and full numerical solutions for the amplitude evolution of both profiles; the wave function and the trapped kink–anti kink. Our results show the significance of permitting longitudinal interactions in the Holstein’s approach to hold trapped localized solutions. It is actually found a critical ratio between longitudinal and on-site interactions, as depending on the velocity of propagation, from where coupled localized solutions exist. •Linear Schrödinger–sine Gordon system as an effective continuum model.•Coupled localized solutions by variational means.•Critical ratio for localized formation.•Full numerical evolution of the LS–sG system.