Essential self-adjointness of a discrete magnetic Sch\"{o}dinger operator

TL;DR

This paper proves the essential self-adjointness of a discrete magnetic Schrödinger operator on a combinatorial model of 2D space, using Dezin discretization, ensuring well-defined quantum dynamics.

Contribution

It establishes essential self-adjointness for a semibounded discrete magnetic Schrödinger operator on a combinatorial 2D model, a novel application of Dezin discretization.

Findings

Proves essential self-adjointness of the operator.

Uses Dezin discretization scheme for model construction.

Ensures well-posed quantum dynamics in the discrete setting.

Abstract

We prove essential self-adjointness for a semibounded from below discrete magnetic Schr\"{o}dinger operator in a space that represents a combinatorial model of the two-dimensional Euclidean space. The Dezin discretization scheme is used for constructing a discrete model.