- 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
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- DOI : 10.1016/j.aop.2014.09.003
- ISSN : 0003-4916
- eISSN : 1096-035X
- Web of Science ID : WOS:000346451900014