論文

査読有り
2014年12月

Real-time Feynman path integral with Picard-Lefschetz theory and its applications to quantum tunneling

ANNALS OF PHYSICS
  • Yuya Tanizaki
  • ,
  • Takayuki Koike

351
開始ページ
250
終了ページ
274
記述言語
英語
掲載種別
研究論文(学術雑誌)
DOI
10.1016/j.aop.2014.09.003
出版者・発行元
ACADEMIC PRESS INC ELSEVIER SCIENCE

Picard-Lefschetz theory is applied to path integrals of quantum mechanics, in order to compute real-time dynamics directly. After discussing basic properties of real-time path integrals on Lefschetz thimbles, we demonstrate its computational method in a concrete way by solving three simple examples of quantum mechanics. It is applied to quantum mechanics of a double-well potential, and quantum tunneling is discussed. We identify all of the complex saddle points of the classical action, and their properties are discussed in detail. However a big theoretical difficulty turns out to appear in rewriting the original path integral into a sum of path integrals on Lefschetz thimbles. We discuss generality of that problem and mention its importance. Real-time tunneling processes are shown to be described by those complex saddle points, and thus semi-classical description of real-time quantum tunneling becomes possible on solid ground if we could solve that problem. (C) 2014 Elsevier Inc. All rights reserved.

Web of Science ® 被引用回数 : 53

リンク情報
DOI
https://doi.org/10.1016/j.aop.2014.09.003
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000346451900014&DestApp=WOS_CPL
ID情報
  • DOI : 10.1016/j.aop.2014.09.003
  • ISSN : 0003-4916
  • eISSN : 1096-035X
  • Web of Science ID : WOS:000346451900014

エクスポート
BibTeX RIS