{"title":"Maximal speed of quantum propagation for the Hartree equation","authors":"J. Arbunich, J. Faupin, F. Pusateri, I. Sigal","doi":"10.1080/03605302.2023.2183408","DOIUrl":null,"url":null,"abstract":"Abstract We prove maximal speed estimates for nonlinear quantum propagation in the context of the Hartree equation. More precisely, under some regularity and integrability assumptions on the pair (convolution) potential, we construct a set of energy and space localized initial conditions such that, up to time-decaying tails, solutions starting in this set stay within the light cone of the corresponding initial datum. We quantify precisely the light cone speed, and hence the speed of nonlinear propagation, in terms of the momentum of the initial state.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":"48 1","pages":"542 - 575"},"PeriodicalIF":2.1000,"publicationDate":"2023-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Partial Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/03605302.2023.2183408","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 4
Abstract
Abstract We prove maximal speed estimates for nonlinear quantum propagation in the context of the Hartree equation. More precisely, under some regularity and integrability assumptions on the pair (convolution) potential, we construct a set of energy and space localized initial conditions such that, up to time-decaying tails, solutions starting in this set stay within the light cone of the corresponding initial datum. We quantify precisely the light cone speed, and hence the speed of nonlinear propagation, in terms of the momentum of the initial state.
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This journal aims to publish high quality papers concerning any theoretical aspect of partial differential equations, as well as its applications to other areas of mathematics. Suitability of any paper is at the discretion of the editors. We seek to present the most significant advances in this central field to a wide readership which includes researchers and graduate students in mathematics and the more mathematical aspects of physics and engineering.
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