日  時: 2月12日(水)15時30分~17時00分

講 演 者: Yves Dermenjian 氏 (Aix-Marseille University)

題  目: The guided states of 3D biperiodic Schroedinger operators

要  旨: Let us consider the Laplacian $H_0= - \Delta$ perturbed by a non-positive potential $V$, which is periodic in two directions, and decays in the remaining one, $x_1$. We are interested in the characterization and decay properties of ground states, defined as the eigenfunctions of the reduced operators in the Bloch-Floquet-Gelfand transform, in the periodic variables, of $H = H_0 + V$. If $V$ is sufficiently small and decreases fast enough in the infinite direction $x_1$, we prove that the guided waves are generically characterized by quasi-momenta belonging to some one-dimensional real analytic submanifold of the Brillouin zone. Moreover they decay faster than the inverse polynomial function in the infinite direction. This is a joint work with F. Bentosela, C. Bourrely and E. Soccorsi.

【 場所 】 自然学系D棟 509教室