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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
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References:

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