2014年12月
Real-time Feynman path integral with Picard-Lefschetz theory and its applications to quantum tunneling
ANNALS OF PHYSICS
- ,
- 巻
- 351
- 号
- 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.
- リンク情報
- ID情報
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- DOI : 10.1016/j.aop.2014.09.003
- ISSN : 0003-4916
- eISSN : 1096-035X
- Web of Science ID : WOS:000346451900014