On the guided states of 3D biperiodic Schrödinger operatorsReport as inadecuate




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1 CPT - Centre de Physique Théorique - UMR 7332 2 LATP - Laboratoire d-Analyse, Topologie, Probabilités

Abstract : We consider the Laplacian operator H 0 perturbed by a non-positive potential $V$, which is periodic in two directions, and decays in the remaining one. We are interested in the characterization and decay properties of the guided states, defined as the eigenfunctions of the reduced operators in the Bloch-Floquet-Gelfand transform of H 0+V in the periodic variables. If V is sufficiently small and decreases fast enough in the infinite direction, we prove that, generically, these guided states are characterized by quasi-momenta belonging to some one-dimensional compact real analytic submanifold of the Brillouin zone. Moreover they decay faster than any polynomial function in the infinite direction.

keyword : Schrödinger operator Periodic potential Guided state Limiting absorption principle





Author: François Bentosela - Claude Bourrely - Yves Dermenjian - Eric Soccorsi -

Source: https://hal.archives-ouvertes.fr/



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