arXiv subjects

Vasilevskiy Boris

Publications and source records attributed to Vasilevskiy Boris.

3 recordsLinked to original sources

arXiv2014

The Green's function of a five-point discretization of a two-dimensional finite-gap Schrödinger operator: the case of four singular points of the spectral curve

Consider a five-point discretization of a two-dimensional finite-gap for a fixed energy Schrödinger operator. We construct the Green's function of the operator. In appears as the explicit formula in terms of the integral by the specific contour on the spectral curve of the differential which is constructed by the wave function and its double. The formula is parametrized by the point on the spectral curve and for almost every parameter value it gives the Green's function with known growth at infinity.

math-ph↗

arXiv2014

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

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.

math-ph↗

arXiv2014

The Green's function of a finite-gap Schrödinger operator discretization on a quad graph

We are using the finite-gap approach for the construction of the Schrödinger operator discretization on a quad graph. The latter is represented by a two-dimensional integer sublattice in a $d$-dimensional space. The Green's function of the operator can be posed explicitly as an integral of the differential built by the spectral data, calculated on contours of the special form. We also know the the asymptotics of the achieved function.

math-ph↗