Two-body threshold spectral analysis, the critical case |
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Authors: | Erik Skibsted Xue Ping Wang |
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Institution: | a Institut for Matematiske Fag, Aarhus Universitet, Ny Munkegade 8000 Aarhus C, Denmark b Laboratoire de Mathématiques Jean Leray, UMR CNRS 6629, Université de Nantes, 44322 Nantes Cedex, France |
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Abstract: | We study in dimension d?2 low-energy spectral and scattering asymptotics for two-body d-dimensional Schrödinger operators with a radially symmetric potential falling off like −γr−2, γ>0. We consider angular momentum sectors, labelled by l=0,1,…, for which γ>2(l+d/2−1). In each such sector the reduced Schrödinger operator has infinitely many negative eigenvalues accumulating at zero. We show that the resolvent has a non-trivial oscillatory behaviour as the spectral parameter approaches zero in cones bounded away from the negative half-axis, and we derive an asymptotic formula for the phase shift. |
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Keywords: | Threshold spectral analysis Schrö dinger operator Critical potential Phase shift |
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