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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 $P_0$.

35J10Schrödinger operator
35B34Resonances in solutions of PDE
35B20Perturbations (PDE)
Full Text: DOI
[1] M. Dimassi, M. Zerzeri, A local trace formula for resonances of perturbed periodic Schrödinger operators, J. Funct. Anal., à paraı\hat{}tre · Zbl 1090.35065
[2] Nedelec, L.: Localisation of resonances for matrix Schrödinger operators. Duke math. J. 106, No. 2, 209-236 (2001) · Zbl 1258.35068
[3] Reed, M.; Simon, B.: Methods of modern mathematical physics, analysis operators. (1978) · Zbl 0401.47001
[4] J. Sjöstrand, A trace formula for resonances and application to semi-classical Schrödinger operators, Séminaire équations aux dérivées partielles, Exposé no 11 (1996--97)