Nonexponential decay laws in perturbation theory of near threshold eigenvalues

We consider a two channel model of the form H-epsilon=[0 H-op E-0 0] +epsilon[W-12 0 0 W-21] on H = H-op circle plus C. The operator H-op is assumed to have the properties of a Schrodinger operator in odd dimensions, with a threshold at zero. As the energy parameter E0 is tuned past the threshold, we consider the survival probability vertical bar vertical bar(2), where Psi(0) is the eigenfunction corresponding to eigenvalue E-0 for epsilon=0. We find nonexponential decay laws for epsilon small and E-0 close to zero provided that the resolvent of Hop is not at least Lipschitz continuous at the threshold zero. (C) 2009 American Institute of Physics. [DOI: 10.1063/1.3046562]