{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T16:17:50Z","timestamp":1762273070673,"version":"build-2065373602"},"reference-count":45,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,4,27]],"date-time":"2023-04-27T00:00:00Z","timestamp":1682553600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004837","name":"MICINN","doi-asserted-by":"publisher","award":["PID2019-109175GB-C22","US-1380977","VIIPPITUS 2023","1.1.1.2\/VIAA\/4\/20\/617","N. 1.1.1.2\/16\/I\/001"],"award-info":[{"award-number":["PID2019-109175GB-C22","US-1380977","VIIPPITUS 2023","1.1.1.2\/VIAA\/4\/20\/617","N. 1.1.1.2\/16\/I\/001"]}],"id":[{"id":"10.13039\/501100004837","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Junta de Andaluc\u00eda","award":["PID2019-109175GB-C22","US-1380977","VIIPPITUS 2023","1.1.1.2\/VIAA\/4\/20\/617","N. 1.1.1.2\/16\/I\/001"],"award-info":[{"award-number":["PID2019-109175GB-C22","US-1380977","VIIPPITUS 2023","1.1.1.2\/VIAA\/4\/20\/617","N. 1.1.1.2\/16\/I\/001"]}]},{"DOI":"10.13039\/100009042","name":"Universidad de Sevilla","doi-asserted-by":"publisher","award":["PID2019-109175GB-C22","US-1380977","VIIPPITUS 2023","1.1.1.2\/VIAA\/4\/20\/617","N. 1.1.1.2\/16\/I\/001"],"award-info":[{"award-number":["PID2019-109175GB-C22","US-1380977","VIIPPITUS 2023","1.1.1.2\/VIAA\/4\/20\/617","N. 1.1.1.2\/16\/I\/001"]}],"id":[{"id":"10.13039\/100009042","id-type":"DOI","asserted-by":"publisher"}]},{"name":"\u201cPost-doctoral Research Aid\u201d of the Republic of Latvia","award":["PID2019-109175GB-C22","US-1380977","VIIPPITUS 2023","1.1.1.2\/VIAA\/4\/20\/617","N. 1.1.1.2\/16\/I\/001"],"award-info":[{"award-number":["PID2019-109175GB-C22","US-1380977","VIIPPITUS 2023","1.1.1.2\/VIAA\/4\/20\/617","N. 1.1.1.2\/16\/I\/001"]}]},{"DOI":"10.13039\/501100008530","name":"European Regional Development Fund","doi-asserted-by":"publisher","award":["PID2019-109175GB-C22","US-1380977","VIIPPITUS 2023","1.1.1.2\/VIAA\/4\/20\/617","N. 1.1.1.2\/16\/I\/001"],"award-info":[{"award-number":["PID2019-109175GB-C22","US-1380977","VIIPPITUS 2023","1.1.1.2\/VIAA\/4\/20\/617","N. 1.1.1.2\/16\/I\/001"]}],"id":[{"id":"10.13039\/501100008530","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we study the spectral properties of polarobreathers, that is, breathers carrying charge in a one-dimensional semiclassical model. We adapt recently developed numerical methods that preserve the charge probability at every step of time integration without using the Born\u2013Oppenheimer approximation, which is the assumption that the electron is not at equilibrium with the atoms or ions. We develop an algorithm to obtain exact polarobreather solutions. The properties of polarobreathers, both stationary and moving ones, are deduced from the lattice and charge variable spectra in the frequency\u2013momentum space. We consider an efficient approach to produce approximate polarobreathers with long lifespans. Their spectrum allows for the determination of the initial conditions and the necessary parameters to obtain numerically exact polarobreathers. The spectra of exact polarobreathers become extremely simple and easy to interpret. We also solve the problem that the charge frequency is not an observable, but the frequency of the charge probability certainly is an observable.<\/jats:p>","DOI":"10.3390\/axioms12050437","type":"journal-article","created":{"date-parts":[[2023,4,28]],"date-time":"2023-04-28T02:02:23Z","timestamp":1682647343000},"page":"437","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Spectral Properties of Exact Polarobreathers in Semiclassical Systems"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6583-6114","authenticated-orcid":false,"given":"Juan F. R.","family":"Archilla","sequence":"first","affiliation":[{"name":"Group of Nonlinear Physics, Universidad de Sevilla, ETSII, Avda Reina Mercedes s\/n, 41012 Sevilla, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7601-8694","authenticated-orcid":false,"given":"J\u0101nis","family":"Baj\u0101rs","sequence":"additional","affiliation":[{"name":"Faculty of Physics, Mathematics and Optometry, University of Latvia, Jelgavas Street 3, LV-1004 Riga, Latvia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,27]]},"reference":[{"key":"ref_1","first-page":"664","article-title":"Electron motion in crystal lattices","volume":"3","author":"Landau","year":"1933","journal-title":"Phys. Z. Sowjetunion"},{"key":"ref_2","first-page":"419","article-title":"Effective mass of a polaron","volume":"18","author":"Landau","year":"1948","journal-title":"Zh. Eksp. Teor. 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