{"title":"霍尔施泰因方法中周期性现场和线性声势相互作用的能量转移","authors":"Sergio Reza-Mejía , Luis A. Cisneros-Ake","doi":"10.1016/j.wavemoti.2024.103382","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"130 ","pages":"Article 103382"},"PeriodicalIF":2.1000,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Energy transfer in the Holstein approach for the interplay between periodic on-site and linear acoustic potentials\",\"authors\":\"Sergio Reza-Mejía , Luis A. Cisneros-Ake\",\"doi\":\"10.1016/j.wavemoti.2024.103382\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>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.</p></div>\",\"PeriodicalId\":49367,\"journal\":{\"name\":\"Wave Motion\",\"volume\":\"130 \",\"pages\":\"Article 103382\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-07-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Wave Motion\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0165212524001124\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ACOUSTICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Wave Motion","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0165212524001124","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ACOUSTICS","Score":null,"Total":0}
Energy transfer in the Holstein approach for the interplay between periodic on-site and linear acoustic potentials
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.
期刊介绍:
Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics.
The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.