Physical Observables for Noncommutative Landau Levels

TL;DR

This paper explores how noncommutative geometry modifies Landau levels in quantum mechanics, affecting physical observables and leading to fractional quantum Hall-like states with an effective magnetic field.

Contribution

It introduces a deformation of the Landau level algebra for noncommutative planes and defines physical observables within this framework, revealing new fractional filling phenomena.

Findings

Deformation alters the effective magnetic field experienced by particles.

Physical observables like density correlation functions are defined in the deformed setting.

Results suggest a connection to fractional quantum Hall states.

Abstract

The Quantum Mechanics of a point particle on a Noncommutative Plane in a magnetic field is implemented in the present work as a deformation of the algebra which defines the Landau levels. I show how to define, in this deformed Quantum Mechanics, the physical observables, like the density correlation functions and Green function, on the completely filled ground level. Also it will be shown that the deformation changes the effective magnetic field which acts on the particles at long range, leading to an incompressible fluid with fractional filling of Laughlin type.