Nonexponential decay laws in perturbation theory of near threshold eigenvalues
- CAQP, Faculty of Physics, University of Bucharest, P.O. Box MG 11, RO-077125 Bucharest (Romania)
- Department of Mathematical Sciences, Aalborg University, Fr. Bajers Vej 7G, DK-9220 Aalborg O (Denmark)
- CAQP, Faculty of Physics, University of Bucharest, P.O. Box MG 11, RO-077125 Bucharest, Romania and Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO-014700 Bucharest (Romania)
We consider a two channel model of the form H{sub {epsilon}}=[(H{sub op}/0)(0/E{sub 0})]+{epsilon}[(0/W{sub 12})(W{sub 21}/0)] on H=H{sub op}+C. The operator H{sub op} is assumed to have the properties of a Schroedinger operator in odd dimensions, with a threshold at zero. As the energy parameter E{sub 0} is tuned past the threshold, we consider the survival probability |<{psi}{sub 0},e{sup -itH}{sub {epsilon}}{psi}{sub 0}>|{sup 2}, where {psi}{sub 0} is the eigenfunction corresponding to eigenvalue E{sub 0} for {epsilon}=0. We find nonexponential decay laws for {epsilon} small and E{sub 0} close to zero provided that the resolvent of H{sub op} is not at least Lipschitz continuous at the threshold zero.
- OSTI ID:
- 21175900
- Journal Information:
- Journal of Mathematical Physics, Vol. 50, Issue 1; Other Information: DOI: 10.1063/1.3046562; (c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
Similar Records
On a Riesz basis of exponentials related to the eigenvalues of an analytic operator and application to a non-selfadjoint problem deduced from a perturbation method for sound radiation
On a Riesz basis of exponentials related to the eigenvalues of an analytic operator and application to a non-selfadjoint problem deduced from a perturbation method for sound radiation