Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8202203 | Annals of Physics | 2014 | 25 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Physics and Astronomy
Physics and Astronomy (General)
Authors
Yuya Tanizaki, Takayuki Koike,