×

Lower bounds for the counting function of resonances for a perturbation of a periodic Schrödinger operator by decreasing potential. (English) Zbl 1032.35063

Summary: We are interested here in the counting function of resonances \(N(h)\) for a perturbation of a periodic Schrödinger operator \(P_0\) by decreasing potential \(W(hx)\) \((h\searrow 0)\). We obtain a lower bound for \(N(h)\) near some singularities of the density of states measure, associated to the unperturbed Hamiltonian \(P_0\).

MSC:

35J10 Schrödinger operator, Schrödinger equation
35B34 Resonance in context of PDEs
35B20 Perturbations in context of PDEs
PDFBibTeX XMLCite
Full Text: DOI

References:

[2] Nedelec, L., Localisation of resonances for matrix Schrödinger operators, Duke Math. J., 106, 2, 209-236 (2001) · Zbl 1258.35068
[3] Reed, M.; Simon, B., Methods of Modern Mathematical Physics, Analysis Operators (1978), Academic Press: Academic Press New York · Zbl 0401.47001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.