Work

On a discrete Schrödinger equation for a quantum dot with a nonlocal potential

Year: 2024

Type: article

Abstract: The paper considers the discrete Schrödinger equation. This is the characteristic equation for a Schrödinger operator of a certain type. It corresponds to a mathematical model that describes nanoscale devices that regulate electron transport using, for example, the Aharonov–Bohm effect. We study the general spectral properties of the operator, find eigenvalues and resonances, and investigate the scattering problem. In particular, conditions for complete transmission (i.e., transmission with probability equal to one) are found, and the possibility of Fano resonance is indicated.

Source: Izvestiya Instituta Matematiki i Informatiki Udmurt Gos Univ

DOI: 10.35634/2226-3594-2024-64-04

Author: N.I. Korobeinikova

Institution: Udmurt State University

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4404705382

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