Noncommutative Quantum Hall Effect and Aharonov-Bohm Effect

Abstract

We study a system of electrons moving on a noncommutative plane in the presence of an external magnetic field which is perpendicular to this plane. For generality we assume that the coordinates and the momenta are both noncommutative. We make a transformation from the noncommutative coordinates to a set of commuting coordinates and then we write the Hamiltonian for this system. The energy spectrum and the expectation value of the current can then be calculated and the Hall conductivity can be extracted. We use the same method to calculate the phase shift for the Aharonov-Bohm effect. Precession measurements could allow strong upper limits to be imposed on the noncommutativity coordinate and momentum parameters $\Theta$ and $\Xi$.

9 pages, RevTeX4, references added, small changes in the text

References in corpus (17)

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• Noncommutative Field Theory and Lorentz Violation
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• Hall Effect in Noncommutative Coordinates
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Cited by in corpus (22)

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• Non-commutativity and non-inertial effects on a scalar field in a cosmic string space-time. Part 2: Spin-zero Duffin-Kemmer-Petiau-like oscillator
• Noncommutative Dirac and Klein-Gordon oscillators in the background of cosmic string: spectrum and dynamics
• Non-commutativity and non-inertial effects on the Dirac oscillator in a cosmic string space-time
• Non-commutativity and non-inertial effects on a scalar field in a cosmic string space-time. Part 1: Klein-Gordon oscillator
• Thermodynamics of a charged particle in a noncommutative plane in a background magnetic field
• Path integral action of a particle in a magnetic field in the noncommutative plane and the Aharonov-Bohm effect
• Analogue of the quantum Hall effect for neutral particles with magnetic dipole moment
• Gauge invariant energy spectra in 2-dimensional noncommutative quantum mechanics
• The Casimir force between parallel plates in Randall-Sundrum I model
• Energy corrections due to the noncommutative phase-space of the charged isotropic harmonic oscillator in a uniform magnetic field in 3D
• The Casimir force on a piston at finite temperature in Randall-Sundrum models
• Propagation of spinors on a noncommutative spacetime: equivalence of the formal and the effective approach
• Coherent states for a system of an electron moving on plane
• Noncommutative Landau problem in graphene: a gauge-invariant analysis with the Seiberg-Witten map
• Pair production of Dirac particles in a d+1-dimensional noncommutative space-time
• Dynamic and static properties of Quantum Hall and Harmonic Oscillator systems on the non-commutative plane
• Energy corrections due to the Non-commutative Phase-Space of the Charged Harmonic Oscillator in a constant magnetic field in 3D