Continuum limits for lattice Schrödinger equations

Hiroshi Isozaki
University of Tsukuba

Date(s) : 14/02/2023   iCal
11 h 00 min - 12 h 00 min

We consider the behavior of solutions of the Helmholtz equation

$(- \Delta_{disc,h} – E)u_h = f_h$ for a continuous spectrum $E$ on a periodic lattice as the mesh size $h$ tends to 0. For the case of the hexagonal and related lattices, in a suitable energy region, it converges to that for the Dirac equation. For the case of the square lattice, triangular lattice, hexagonal lattice (in another energy region) and subdivision of a square lattice, one can add a scalar potential, and the solution of the lattice Schr{\”o}dinger equation $( – \Delta_{disc,h} +V_{disc,h} – E)u_h = f_h$ converges to that of the continuum Schrödinger equation $(P(D_x) + V(x) -E)u = f$. This is a joint work with A. Jensen.


Site Nord, CMI, Salle de Séminaire R164 (1er étage)


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