{"id":17460,"date":"2023-07-29T10:25:05","date_gmt":"2023-07-29T01:25:05","guid":{"rendered":"https:\/\/www.waseda.jp\/fsci\/mathphys\/?p=17460"},"modified":"2023-12-05T11:47:02","modified_gmt":"2023-12-05T02:47:02","slug":"%e7%89%b9%e5%88%a5%e8%ac%9b%e7%be%a9%e3%80%8ca-mean-field-limit-of-quantum-many-body-dynamics-i-and-ii%e3%80%8d%e9%96%8b%e5%82%ac","status":"publish","type":"post","link":"https:\/\/www.waseda.jp\/fsci\/mathphys\/news\/17460","title":{"rendered":"\u7279\u5225\u8b1b\u7fa9\u300cMean-field limits of quantum many-body dynamics I and II\u300d\u958b\u50ac"},"content":{"rendered":"<p>\u6570\u7269\u7cfb\u79d1\u5b66\u62e0\u70b9\u3067\u306f\u3001\u56fd\u969b\u6559\u80b2\u6d3b\u52d5\u306e\u4e00\u74b0\u3068\u3057\u3066\u4e0b\u8a18\u7279\u5225\u8b1b\u7fa9\u3092\u958b\u50ac\u3057\u307e\u3059\u3002\u672c\u8b1b\u7fa9\u3067\u306f\u3001\u96e2\u6563\u30df\u30af\u30ed\u30e2\u30c7\u30eb\u304b\u3089\u9023\u7d9a\u30de\u30af\u30ed\u30e2\u30c7\u30eb\u306e\u5c0e\u51fa\u65b9\u6cd5\u3092\u6700\u8fd1\u306e\u7814\u7a76\u7d50\u679c\u3082\u542b\u3093\u3060\u5f62\u3067\u57fa\u672c\u304b\u3089\u89e3\u8aac\u3057\u307e\u3059\u3002<\/p>\n<h3>\u65e5\u7a0b<\/h3>\n<p>2023\u5e748\u670830\u65e5<\/p>\n<ul>\n<li>10:00 &#8211; 11:30\u3000 Lecture I<\/li>\n<li>14:00 &#8211; 15:30\u3000 Lecture II<\/li>\n<\/ul>\n<h3>\u4f1a\u5834<\/h3>\n<p>\u65e9\u7a32\u7530\u5927\u5b66\u897f\u65e9\u7a32\u7530\u30ad\u30e3\u30f3\u30d1\u30b9\u300062W\u53f7\u9928 1\u968e \u5927\u4f1a\u8b70\u5ba4A\uff08\u6771\u5074\uff09<\/p>\n<h3>\u984c\u76ee\uff0f\u8b1b\u6f14\u6982\u8981<\/h3>\n<h4>Mean-field limits of quantum many-body dynamics I and II<\/h4>\n<p>\u3010\u8b1b\u6f14\u6982\u8981\u3011<\/p>\n<p>The rigorous justification of mean-field type equations (Boltzmann, Vlasov-Poisson, nonlinear Schr\u00f6dinger&#8230;) from the many-body systems they are supposed to describe is a vast and fundamental subject. In these two lectures, we survey the mathematical achievements in the quantum aspect of the area, mainly regarding the nonlinear Schr\u00f6dinger equation (NLS). Since the Nobel Prize winning first observation of Bose-Einstein condensation (BEC), the investigation of the new state of matter and thus NLS has become a research hot spot and seen vast developments in recent years. At the same time, the study of many-body dynamics feeds back into the study of the corresponding mean-field equations. We discuss such a derivation in the energy-critical setting which also yields a solution to a problem raised by T. Kato.<\/p>\n<h3>\u8b1b\u5e2b<\/h3>\n<div id=\"attachment_17473\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-17473 size-full\" src=\"https:\/\/www.waseda.jp\/fsci\/mathphys\/assets\/uploads\/2023\/07\/Photo_Xuwen_Chen.jpg\" alt=\"\" width=\"200\" height=\"240\" \/><p class=\"wp-caption-text\"><a href=\"https:\/\/people.math.rochester.edu\/faculty\/xchen84\/\" target=\"_blank\" rel=\"noopener\">Xuwen Chen <\/a> ( Department of Mathematics, University of Rochester, Professor)<\/p><\/div>\n<h3>\u8a00\u8a9e<\/h3>\n<p>\u82f1\u8a9e<\/p>\n<h3>\u5bfe\u8c61<\/h3>\n<p>\u5b66\u751f\u3001\u7814\u7a76\u8005<\/p>\n<h3>\u4e8b\u524d\u767b\u9332<\/h3>\n<p>\u4e0d\u8981<\/p>\n<h3>\u304a\u554f\u5408\u305b<\/h3>\n<p>\u65e9\u7a32\u7530\u5927\u5b66 \u57fa\u5e79\u7406\u5de5\u5b66\u90e8 \u6570\u5b66\u79d1 \u798f\u6cc9\u9e97\u4f73 \u6559\u6388<br \/>\nfukuizumi [AT] waseda.jp<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6570\u7269\u7cfb\u79d1\u5b66\u62e0\u70b9\u3067\u306f\u3001\u56fd\u969b\u6559\u80b2\u6d3b\u52d5\u306e\u4e00\u74b0\u3068\u3057\u3066\u4e0b\u8a18\u7279\u5225\u8b1b\u7fa9\u3092\u958b\u50ac\u3057\u307e\u3059\u3002\u672c\u8b1b\u7fa9\u3067\u306f\u3001\u96e2\u6563\u30df\u30af\u30ed\u30e2\u30c7\u30eb\u304b\u3089\u9023\u7d9a\u30de\u30af\u30ed\u30e2\u30c7\u30eb\u306e\u5c0e\u51fa\u65b9\u6cd5\u3092\u6700\u8fd1\u306e\u7814\u7a76\u7d50\u679c\u3082\u542b\u3093\u3060\u5f62\u3067\u57fa\u672c\u304b\u3089\u89e3\u8aac\u3057\u307e\u3059\u3002 \u65e5\u7a0b 2023\u5e748\u670830\u65e5 10:00 &#038; [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":17476,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[1],"tags":[53,139,162],"class_list":["post-17460","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-news","tag-events","tag-lecture","tag-education"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/posts\/17460","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/comments?post=17460"}],"version-history":[{"count":2,"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/posts\/17460\/revisions"}],"predecessor-version":[{"id":18386,"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/posts\/17460\/revisions\/18386"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/media\/17476"}],"wp:attachment":[{"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/media?parent=17460"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/categories?post=17460"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/tags?post=17460"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}