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Title: Determination of the border between 'shallow' and 'deep' tunneling regions for the Herman-Kluk method by the asymptotic approach

Abstract

The evaluation of a tunneling tail by the Herman-Kluk method, which is a quasiclassical way to compute quantum dynamics, is examined by asymptotic analysis. In the shallower part of the tail, as well as in the classically allowed region, it is shown that the leading terms of semiclassical evaluations of quantum theory and the Herman-Kluk formula agree, which is known as an asymptotic equivalence. In the deeper part, it is shown that the asymptotic equivalence breaks down, due to the emergence of unusual 'tunneling trajectory', which is an artifact of the Herman-Kluk method.

Authors:
 [1]
  1. Department of Physics, Tokyo Metropolitan University, Minami-Osawa, Hachioji, Tokyo 192-0397 (Japan)
Publication Date:
OSTI Identifier:
20979316
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.73.024101; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPUTER CALCULATIONS; EVALUATION; QUANTUM ELECTRODYNAMICS; QUANTUM FIELD THEORY; SEMICLASSICAL APPROXIMATION; SIMULATION; TUNNEL EFFECT

Citation Formats

Tanaka, Atushi. Determination of the border between 'shallow' and 'deep' tunneling regions for the Herman-Kluk method by the asymptotic approach. United States: N. p., 2006. Web. doi:10.1103/PHYSREVA.73.024101.
Tanaka, Atushi. Determination of the border between 'shallow' and 'deep' tunneling regions for the Herman-Kluk method by the asymptotic approach. United States. doi:10.1103/PHYSREVA.73.024101.
Tanaka, Atushi. Wed . "Determination of the border between 'shallow' and 'deep' tunneling regions for the Herman-Kluk method by the asymptotic approach". United States. doi:10.1103/PHYSREVA.73.024101.
@article{osti_20979316,
title = {Determination of the border between 'shallow' and 'deep' tunneling regions for the Herman-Kluk method by the asymptotic approach},
author = {Tanaka, Atushi},
abstractNote = {The evaluation of a tunneling tail by the Herman-Kluk method, which is a quasiclassical way to compute quantum dynamics, is examined by asymptotic analysis. In the shallower part of the tail, as well as in the classically allowed region, it is shown that the leading terms of semiclassical evaluations of quantum theory and the Herman-Kluk formula agree, which is known as an asymptotic equivalence. In the deeper part, it is shown that the asymptotic equivalence breaks down, due to the emergence of unusual 'tunneling trajectory', which is an artifact of the Herman-Kluk method.},
doi = {10.1103/PHYSREVA.73.024101},
journal = {Physical Review. A},
number = 2,
volume = 73,
place = {United States},
year = {Wed Feb 15 00:00:00 EST 2006},
month = {Wed Feb 15 00:00:00 EST 2006}
}
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