Hakim Boumaza (Paris)

Title: Integrated density of states of the periodic Airy-Schrödinger operator
Abstract: In this talk I present, in the semiclassical regime, an explicit formula for the integrated density of states of the periodic Airy-Schrodinger operator on the real line. The potential of this Schrödinger operator is periodic, continuous and piecewise linear. For this purpose, the spectrum of the Schrödinger operator whose potential is the restriction of the periodic Airy-Schrödinger potential to a finite number of periods is studied. We prove that all the eigenvalues of the operator corresponding to the restricted potential are in the spectral bands of the periodic Airy-Schrodinger operator and none of them are in its spectral gaps. In the semiclassical regime, we count the number of these eigenvalues in each of the spectral bands. Note that in these results there are explicit constants which characterize the semiclassical regime. This is joint work with Olivier Lafitte (USPN - CRM Montreal).

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