Resonantstate expansions and the longtime behavior of quantum decay
Abstract
It is shown that a representation of the decaying wave function as a resonant sum plus a nonexponential integral term may be written as a purely discrete resonant sum by evaluating at long times the integral term by the steepest descents method, and then expanding the resulting expression in terms of resonant states. This leads to a representation that is valid along the exponential and the inverse power in time regimes. A model calculation using the {delta} potential allows us to make a comparison of the expansion with numerical integrations in terms of continuum wave functions and, in the long time regime, with an exact analytic expression of the integral term obtained using the steepest descents method. The results demonstrate that resonant states give a correct description of the longtime behavior of decay.
 Authors:
 Instituto de Fisica, Universidad Nacional Autonoma de Mexico, Apartado Postal 20 364, 01000 Mexico, Distrito Federal (Mexico)
 Centro de Investigacion Cientifica y de Educacion Superior de Ensenada, Apartado Postal 2372, 22860 Ensenada, Baja California (Mexico)
 Instituto de Ciencia de Materiales de Madrid (CSIC), Cantoblanco, 28049 Madrid (Spain)
 Publication Date:
 OSTI Identifier:
 21011150
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. A; Journal Volume: 76; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevA.76.012103; (c) 2007 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; COMPARATIVE EVALUATIONS; DECAY; EXPANSION; MATHEMATICAL MODELS; POTENTIALS; PROBABILITY; RESONANCE; SIMULATION; WAVE FUNCTIONS
Citation Formats
GarciaCalderon, Gaston, Maldonado, Irene, and Villavicencio, Jorge. Resonantstate expansions and the longtime behavior of quantum decay. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.76.012103.
GarciaCalderon, Gaston, Maldonado, Irene, & Villavicencio, Jorge. Resonantstate expansions and the longtime behavior of quantum decay. United States. doi:10.1103/PHYSREVA.76.012103.
GarciaCalderon, Gaston, Maldonado, Irene, and Villavicencio, Jorge. Sun .
"Resonantstate expansions and the longtime behavior of quantum decay". United States.
doi:10.1103/PHYSREVA.76.012103.
@article{osti_21011150,
title = {Resonantstate expansions and the longtime behavior of quantum decay},
author = {GarciaCalderon, Gaston and Maldonado, Irene and Villavicencio, Jorge},
abstractNote = {It is shown that a representation of the decaying wave function as a resonant sum plus a nonexponential integral term may be written as a purely discrete resonant sum by evaluating at long times the integral term by the steepest descents method, and then expanding the resulting expression in terms of resonant states. This leads to a representation that is valid along the exponential and the inverse power in time regimes. A model calculation using the {delta} potential allows us to make a comparison of the expansion with numerical integrations in terms of continuum wave functions and, in the long time regime, with an exact analytic expression of the integral term obtained using the steepest descents method. The results demonstrate that resonant states give a correct description of the longtime behavior of decay.},
doi = {10.1103/PHYSREVA.76.012103},
journal = {Physical Review. A},
number = 1,
volume = 76,
place = {United States},
year = {Sun Jul 15 00:00:00 EDT 2007},
month = {Sun Jul 15 00:00:00 EDT 2007}
}

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