{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:51:42Z","timestamp":1777449102741,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"3-4","license":[{"start":{"date-parts":[[2013,12,1]],"date-time":"2013-12-01T00:00:00Z","timestamp":1385856000000},"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":[[2013,12]]},"abstract":"<jats:p>\n                    In this paper, we derive a semiclassical asymptotic expansion of the Wick symbol, for the product of two operators, when the first one is a Weyl pseudodifferential operator in the class of Calder\u00f3n\u2013Vaillancourt and the second one is trace class in L\n                    <jats:sup>2<\/jats:sup>\n                    (R\n                    <jats:sup>n<\/jats:sup>\n                    ). This result is extended in the direction of Schatten classes. We also report a corresponding result in the context of anti-Wick operators. The Wick expansion is used to derive an equation satisfied, up to an arbitrary small error term, by the Wick symbol of density operators governed by the time dependent Hartree\u2013Fock (TDHF) equation. Still in the situation of the TDHF dynamics, we prove the finiteness of the Ehrenfest time.\n                  <\/jats:p>","DOI":"10.3233\/asy-131184","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:30:40Z","timestamp":1575055840000},"page":"229-248","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Approximative composition of Wick symbols and applications to the time dependent Hartree\u2013Fock equation"],"prefix":"10.1177","volume":"85","author":[{"given":"L.","family":"Amour","sequence":"first","affiliation":[{"name":"Laboratoire de Math\u00e9matiques de Reims, EA 4535 and FR CNRS-3399, Universit\u00e9 de Reims Champagne-Ardenne, 51687 Reims, France. E-mails: {laurent.amour, khodja, jean.nourrigat}@univ-reims.fr"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"Khodja","sequence":"additional","affiliation":[{"name":"Laboratoire de Math\u00e9matiques de Reims, EA 4535 and FR CNRS-3399, Universit\u00e9 de Reims Champagne-Ardenne, 51687 Reims, France. E-mails: {laurent.amour, khodja, jean.nourrigat}@univ-reims.fr"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J.","family":"Nourrigat","sequence":"additional","affiliation":[{"name":"Laboratoire de Math\u00e9matiques de Reims, EA 4535 and FR CNRS-3399, Universit\u00e9 de Reims Champagne-Ardenne, 51687 Reims, France. E-mails: {laurent.amour, khodja, jean.nourrigat}@univ-reims.fr"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2013,12,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-131184","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-131184","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:40:02Z","timestamp":1777380002000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-131184"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,12]]},"references-count":0,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2013,12]]}},"alternative-id":["10.3233\/ASY-131184"],"URL":"https:\/\/doi.org\/10.3233\/asy-131184","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,12]]}}}