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UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS Guest
2024-11-22 2:33 |
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Conference: Bucharest University Faculty of Physics 2007 Meeting
Section: Quantum Mechanics, Statistical Physics, Optics, Spectroscopy, Plasma and Lasers
Title:
Exponential decay laws in perturbation theory
of threshold and embedded eigenvalues - Invited lecture
Authors:
Gheorghe Nenciu
Affiliation:
Faculty of Physics, CAQP
University of Bucharest
P.O. Box MG 11, RO-077125 Bucharest, Romania
E-mail
Keywords:
Abstract:
Exponential decay laws for the metastable states resulting from perturbation of unstable eigenvalues are discussed. Eigenvalues embedded in the continuum as well as threshold eigenvalues are considered. Stationary methods are used, i.e. the evolution group is written in terms of resolvent via Stone’s formula and a partition technique (Schur-Livsic-Feschbach-Grushin formula) is used to localize the essential terms. No analytic continuation of the resolvent is required. The main result is about the Fermi Golden Rule at threshold: for Schrodinger operators in odd dimensions the leading term of the life-time in the perturbation strength E, is of order E^(2+u/2), where u is an odd integer, u>=−1. Examples covering all values of u are given.
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