Physical Observables for Noncommutative Landau Levels

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.

arXiv comment14 pages, 6 figures, replaced with corrected version as it appears in J.Phys.A

References in corpus (7)

• Quantum mechanics on the noncommutative plane and sphere
• Feynman Path Integral on the Noncommutative Plane
• The exotic Galilei group and the "Peierls substitution"
• Quantum Hall states as matrix Chern-Simons theory
• Exotic galilean symmetry in the non-commutative plane, and the Hall effect
• Infinite Symmetry in the Quantum Hall Effect
• Matrix Model Description of Laughlin Hall States

Cited by in corpus (5)

• Magnetic fields in noncommutative quantum mechanics
• On the Landau system in noncommutative phase-space
• A (p,q)-deformed Landau problem in a spherical harmonic well: spectrum and noncommuting coordinates
• Landau levels in a 2D noncommutative space: matrix and quaternionic vector coherent states
• Energy corrections due to the noncommutative phase-space of the charged isotropic harmonic oscillator in a uniform magnetic field in 3D