Article Dans Une Revue Journal of Mathematical Physics Année : 2021

Integrated density of states: from the finite range to the periodic Airy-Schroedinger operator

Résumé

We compute an explicit formula for the integrated density of states of the periodic Airy-Schrödinger operator on the real line. The potential of this Schrödinger operator is periodic, continuous and piecewise affine. For this purpose, we study precisely the spectrum of the Schrödinger operator whose potential is the restriction of the periodic Airy-Schrödinger potential to a finite number of periods. We prove that all the eigenvalues of the operator corresponding to the restricted potential are in the spectral bands of the periodic Airy-Schrödinger operator and none of them are in its spectral gaps. We count exactly the number of these eigenvalues in each of these spectral bands. Note that our results depend on a semiclassical parameter and are valid for values of it larger than explicit constants.

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hal-02964056 , version 1 (14-10-2020)

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Hakim Boumaza, Olivier Lafitte. Integrated density of states: from the finite range to the periodic Airy-Schroedinger operator. Journal of Mathematical Physics, 2021, 62, pp.043503. ⟨10.1063/5.0015181⟩. ⟨hal-02964056⟩
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