This article is cited in 10 papers

Spectrum of three-dimensional landau operator perturbed by a periodic point potential

V. A. Geiler, V. V. Demidov

Mordovian State University

Abstract: A study is made of a three-dimensional Schrödinger operator with magnetic field and perturbed by a periodic sum of zero-range potentials. In the case of a rational flux, the explicit form of the decomposition of the resolvent of this operator with respect to the spectrum of irreducible representations of the group of magnetic translations is found. In the case of integer flux, the explicit form of the dispersion laws is found, the spectrum is described, and a qualitative investigation of it is made (in particular, it is established that not more than one gap exists).

Received: 07.07.1994

 English version: Theoretical and Mathematical Physics, 1995, 103:2, 561–569

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