{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:55:40Z","timestamp":1777449340136,"version":"3.51.4"},"reference-count":13,"publisher":"SAGE Publications","issue":"1-2","license":[{"start":{"date-parts":[[2016,5,3]],"date-time":"2016-05-03T00:00:00Z","timestamp":1462233600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2016,5,3]]},"abstract":"<jats:p>We consider a class of modified Schr\u00f6dinger operators where the semiclassical Laplacian is perturbed with h-dependent interface conditions occurring at the boundaries of the potential\u2019s support. Under positivity assumptions on the potential, we show that this modification produces a small perturbation on the dynamics as [Formula: see text], independently from the time scale. In the case of a time dependent potential, this yields uniform-in- h stability estimates for products of instantaneous propagators. Then, following a standard approach, the non-autonomous dynamical system is defined as a limit of stepwise propagators and its small- h expansion is provided under suitable regularity assumptions on the potential\u2019s variations.<\/jats:p>","DOI":"10.3233\/asy-161359","type":"journal-article","created":{"date-parts":[[2016,5,3]],"date-time":"2016-05-03T16:44:47Z","timestamp":1462293887000},"page":"1-30","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Non-autonomous quantum systems with scale-dependent interface conditions"],"prefix":"10.1177","volume":"98","author":[{"given":"Andrea","family":"Mantile","sequence":"first","affiliation":[{"name":"Laboratoire de Math\u00e9matiques, Universit\u00e9 de Reims \u2013 FR3399 CNRS, Moulin de la Housse BP 1039, 51687 Reims, France. E-mail:\u00a0"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2016,5,3]]},"reference":[{"key":"ref001","doi-asserted-by":"publisher","DOI":"10.1090\/chel\/350"},{"key":"ref002","doi-asserted-by":"crossref","first-page":"937","DOI":"10.1016\/j.anihpc.2007.05.007","volume":"25","author":"Bonnaillie-No\u00ebl V.","year":"2008","journal-title":"Ann. I.H.P. An. Non Lin\u00e9aire"},{"key":"ref003","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-74751-9"},{"issue":"3","key":"ref004","first-page":"541","volume":"21","author":"Faraj A.","year":"2011","journal-title":"M3AS"},{"key":"ref005","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0741-2"},{"key":"ref006","doi-asserted-by":"publisher","DOI":"10.1006\/aphy.1995.1040"},{"key":"ref007","first-page":"241","volume":"17","author":"Kato T.","year":"1970","journal-title":"J. Fac. Sci. Univ. Tokyo Sect. I"},{"key":"ref008","doi-asserted-by":"publisher","DOI":"10.1063\/1.4817854"},{"key":"ref009","doi-asserted-by":"publisher","DOI":"10.1063\/1.4894058"},{"key":"ref010","doi-asserted-by":"publisher","DOI":"10.1007\/BF02096616"},{"key":"ref011","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160120202"},{"key":"ref012","doi-asserted-by":"publisher","DOI":"10.1090\/surv\/158"},{"key":"ref013","unstructured":"K.Yoshida, Functional Analysis, 2nd edn, Springer-Verlag, Berlin, 1968."}],"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-161359","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/ASY-161359","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-161359","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:40:47Z","timestamp":1777380047000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-161359"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,5,3]]},"references-count":13,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2016,5,3]]}},"alternative-id":["10.3233\/ASY-161359"],"URL":"https:\/\/doi.org\/10.3233\/asy-161359","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,5,3]]}}}