Landau Levels in the noncommutative $AdS_2$

TL;DR

This paper explores the quantum Landau problem on a noncommutative $AdS_2$ surface, deriving its spectrum and comparing it to the classical case, thus extending understanding of quantum behavior in noncommutative curved spaces.

Contribution

It formulates the Landau problem on noncommutative $AdS_2$ and derives the spectrum, providing new insights into quantum effects in noncommutative geometries.

Findings

Spectrum differs from the commutative $AdS_2$ case

Highlights effects of noncommutativity on quantum levels

Provides a foundation for further studies in noncommutative quantum geometry

Abstract

We formulate the Landau problem in the context of the noncommutative analog of a surface of constant negative curvature, that is $AdS_2$ surface, and obtain the spectrum and contrast the same with the Landau levels one finds in the case of the commutative $AdS_2$ space.