A sufficient condition for nonsingularity of two-dimensional finite-gap Schrödinger operator discretization of a quad graph

2014/02/09 by Boris, Vasilevskiy
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1402.1938

Abstract

We construct a two-dimensional Schrödinger operator on a quad-graph using finite-gap approach. A guad-graph is a planar graph with only 4-sided faces. We define the non-singularity of the operator as the positivity of all of his coefficients. At last, we prove some sufficient conditions of such positivity on the spectral curve and the graph.

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