{"title":"The Random Schroźdinger Equation","authors":"Yu Gu, L. Ryzhik","doi":"10.1137/15M1024986","DOIUrl":null,"url":null,"abstract":"We analyze the solutions of the Schroźdinger equation with low frequency initial data and a time-dependent weakly random potential. We prove a homogenization result for the low frequency component of the wave field. We also show that the dynamics generates a nontrivial energy in the high frequencies, which does not homogenize---the high frequency component of the wave field remains random and the evolution of its energy is described by a kinetic equation. The transition from the homogenization of the low frequencies to the random limit of the high frequencies is illustrated by understanding the size of the small random fluctuations of the low frequency component.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1137/15M1024986","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/15M1024986","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 3
Abstract
We analyze the solutions of the Schroźdinger equation with low frequency initial data and a time-dependent weakly random potential. We prove a homogenization result for the low frequency component of the wave field. We also show that the dynamics generates a nontrivial energy in the high frequencies, which does not homogenize---the high frequency component of the wave field remains random and the evolution of its energy is described by a kinetic equation. The transition from the homogenization of the low frequencies to the random limit of the high frequencies is illustrated by understanding the size of the small random fluctuations of the low frequency component.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
