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CANCELLED Lattice Hamiltonians and their continuum limit

Hiroshi Isozaki (Graduate School of Pure and Applied Sciences, University of Tsukuba)
Thursday 12 March 2020 16:15–17:00 Aud. D3 (1531-215)
Mathematics Seminar

Discrete operators (i.e. difference operators) are often introduced as an approximation of differential operators. However, if we start form the discrete model, it is not obvious that discrete systems have continuum limits as the mesh size tends to 0. In this talk, we show that on physically important lattices, e.g. the square, triangular, hexagonal lattices, the solutions for the stationary Schroedinger equations associated to the continuous spectrum converge to those for the continuous model. In particular, we can deal with graphen and graphite. Our solutions satisfy the radiation condition, hence they describe the scattering phenomena. In the case of the hexagonal lattice, one can derive both of Schroedinger equations and Dirac equations according to the energy.

This is a joint work with Arne Jensen in Aalborg.

Contact: Erik Skibsted Revised: 25.05.2023