{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:49:56Z","timestamp":1777448996907,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"1-2","license":[{"start":{"date-parts":[[2012,10,1]],"date-time":"2012-10-01T00:00:00Z","timestamp":1349049600000},"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":[[2012,10]]},"abstract":"<jats:p>In this paper, we study the scattering theory for a 2\u00d72 matrix Schr\u00f6dinger operator<\/jats:p>\n                  <jats:p>\n                    P=\u2212h\n                    <jats:sup>2<\/jats:sup>\n                    d\n                    <jats:sup>2<\/jats:sup>\n                    \/dx\n                    <jats:sup>2<\/jats:sup>\n                    I\n                    <jats:sub>2<\/jats:sub>\n                    +V(x)+hR(x,hD\n                    <jats:sub>x<\/jats:sub>\n                    )\n                  <\/jats:p>\n                  <jats:p>\n                    on L\n                    <jats:sup>2<\/jats:sup>\n                    (R)\u2316L\n                    <jats:sup>2<\/jats:sup>\n                    (R), where V(x) is a real diagonal matrix, the eigenvalues of which are never equal. Under some assumptions of analyticity and decay at infinity of V, we describe the asymptotic behavior of the scattering matrix S=(s\n                    <jats:sub>ij<\/jats:sub>\n                    )\n                    <jats:sub>1\u2264i,j\u22644<\/jats:sub>\n                    associated with P when the semi-classical parameter h goes to zero. Moreover, we obtain the estimate\n                  <\/jats:p>\n                  <jats:p>\n                    \u2016S\n                    <jats:sub>12<\/jats:sub>\n                    \u2016+\u2016S\n                    <jats:sub>21<\/jats:sub>\n                    \u2016=O(e\n                    <jats:sup>\u2212\u03b4\/h<\/jats:sup>\n                    ),\n                  <\/jats:p>\n                  <jats:p>\n                    where S\n                    <jats:sub>12<\/jats:sub>\n                    and S\n                    <jats:sub>21<\/jats:sub>\n                    are the two off-diagonal elements of S and \u03b4&gt;0 is a constant which is explicitly related to the behavior of V(x) in the complex domain.\n                  <\/jats:p>","DOI":"10.3233\/asy-2012-1105","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:23:20Z","timestamp":1575055400000},"page":"57-78","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["Asymptotic expansion of the scattering matrix associated with matrix Schr\u00f6dinger operator"],"prefix":"10.1177","volume":"80","author":[{"given":"Hamadi","family":"Baklouti","sequence":"first","affiliation":[{"name":"D\u00e9pt de Maths, FSS, Universit\u00e9 de Sfax, Sfax, Tunisie. E-mail: h.baklouti@gmail.com"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Slaheddine Ben","family":"Abdeljeilil","sequence":"additional","affiliation":[{"name":"D\u00e9pt de Maths, FST, Universit\u00e9 de Tunis, Tunis, Tunisie. E-mail: sabdejlil@yahoo.fr"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2012,10,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2012-1105","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2012-1105","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:39:42Z","timestamp":1777379982000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-2012-1105"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,10]]},"references-count":0,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2012,10]]}},"alternative-id":["10.3233\/ASY-2012-1105"],"URL":"https:\/\/doi.org\/10.3233\/asy-2012-1105","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,10]]}}}