A Quantum Dot with Impurity in the Lobachevsky Plane

TL;DR

This paper studies how curvature influences a quantum dot with impurity on the Lobachevsky plane, providing explicit solutions for the Green function and Krein Q-function to understand the system's properties.

Contribution

It introduces an exactly solvable model of a quantum dot with impurity on a curved Lobachevsky plane, analyzing curvature effects on quantum confinement.

Findings

Explicit Green function and Krein Q-function derived

Curvature significantly affects quantum dot properties

Model provides insights into quantum systems on curved surfaces

Abstract

The curvature effect on a quantum dot with impurity is investigated. The model is considered on the Lobachevsky plane. The confinement and impurity potentials are chosen so that the model is explicitly solvable. The Green function as well as the Krein Q-function are computed.