The Landau problem and noncommutative quantum mechanics

Abstract

The conditions under which noncommutative quantum mechanics and the Landau problem are equivalent theories is explored. If the potential in noncommutative quantum mechanics is chosen as $V=\Omega \aleph$ with $\aleph$ defined in the text, then for the value $\tilde{\theta }=0.22\times 10^{-11}c{m}^2$ (that measures the noncommutative effects of the space), the Landau problem and noncommutative quantum mechanics are equivalent theories in the lowest Landau level. For other systems one can find differents values for $\tilde{\theta }$ and, therefore, the possible bounds for $\tilde{\theta }$ should be searched in a physical independent scenario. This last fact could explain the differents bounds for $\tilde{\theta }$ found in the literature.

This a rewritten and corrected version of our previous preprint hep-th/0105173

Cited by in corpus (89)

• Spin Hall effect and Berry phase of spinning particles
• Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces
• Hall Effect in Noncommutative Coordinates
• Testing spatial noncommutativiy via the Aharonov-Bohm effect
• Noncommutative Quantum Mechanics: The Two-Dimensional Central Field
• A comparative review of four formulations of noncommutative quantum mechanics
• The Aharonov-Bohm Effect in Noncommutative Quantum Mechanics
• Noncommutative quantum mechanics and the Aharonov-Casher effect
• On noncommutative isotropic harmonic oscillator
• Composite system in noncommutative space and the equivalence principle
• Monopole and Berry Phase in Momentum Space in Noncommutative Quantum Mechanics
• Noncommutative 3D harmonic oscillator
• Magnetic fields in noncommutative quantum mechanics
• Noncommutative Dirac oscillator in an external magnetic field
• Noncommutative oscillator, symmetry and Landau problem
• Magnetic-Dipole Spin Effects in Noncommutative Quantum Mechanics
• Probing phase-space noncommutativity through quantum beating, missing information and the thermodynamic limit
• Towards a Noncommutative Astrophysics
• Landau Problem in Noncommutative Quantum Mechanics
• Landau Analog Levels for Dipoles in the Noncommutative Space and Phase Space
• Harmonic oscillator in a background magnetic field in noncommutative quantum phase-space
• Aharonov-Bohm effect in a Class of Noncommutative Theories
• Exact solution of two dimensional Dunkl harmonic oscillator in Non-Commutative phase-space
• Quantum phase transitions in the noncommutative Dirac Oscillator
• Probing phase-space noncommutativity through quantum mechanics and thermodynamics of free particles and quantum rotors
• Aharonov-Casher effect for spin one particles in a noncommutative space
• On uncertainty relations in noncommutative quantum mechanics
• On the Landau system in noncommutative phase-space
• Probing spacetime noncommutative constant via charged astrophysical black hole lensing
• Phase-space noncommutative extension of the Robertson-Schroedinger formulation of Ozawa's uncertainty principle
• Supersymmetric Quantum Mechanics on Non-Commutative Plane
• Exact master equation for a noncommutative Brownian particle
• Non-singular Brans-Dicke collapse in deformed phase space
• Thermodynamics of Quantum Phase Transitions of a Dirac oscillator in a homogenous magnetic field
• Electron dynamics in noncommutative geometry with magnetic field and Zitterbewegung phenomenon
• Effect of noncommutativity on the spectrum of free particle and harmonic oscillator in rotationally invariant noncommutative phase space
• Quantum engines and the range of the second law of thermodynamics in the noncommutative phase-space
• Non-commutative Supersymmetric Quantum Mechanics
• Angular momentum quantum backflow in the noncommutative plane
• Kinematic variables in noncommutative phase space and parameters of noncommutativity
• Pauli Oscillator In Noncommutative Space
• Non-commutativity and non-inertial effects on the Dirac oscillator in a cosmic string space-time
• Noncommutative phase space with rotational symmetry and hydrogen atom
• Stability Conditions For a Noncommutative Scalar Field Coupled to Gravity
• Chiral bosonization for non-commutative fields
• Noncommutativity in (2+1)-dimensions and the Lorentz group
• Rotationally invariant noncommutative phase space of canonical type with recovered weak equivalence principle
• Berry's phase in noncommutative spaces
• Spin Non-commutativity and the Three-Dimensional Harmonic Oscillator
• A (p,q)-deformed Landau problem in a spherical harmonic well: spectrum and noncommuting coordinates
• Commutator Anomaly in Noncommutative Quantum Mechanics
• Gaussian fidelity distorted by external fields
• Noncommutative Quantum Cosmology
• On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space
• Magnetic Seed and Cosmology as Quantum Hall Effect
• Coherent quantum squeezing due to the phase space noncommutativity
• Noncommutative geometry induced by spin effects
• From Feynman Proof of Maxwell Equations to Noncommutative Quantum Mechanics
• Non-Commutativity effects in the Dirac equation in crossed electric and magnetic fields
• Noncommutative massive Thirring model in three-dimensional spacetime
• Deformed classical-quantum mechanics transition
• Generalized Toda mechanics associated with classical Lie algebras and their reductions
• Features of free particles system motion in noncommutative phase space
• Scattering in Noncommutative Quantum Mechanics
• Landau levels in a 2D noncommutative space: matrix and quaternionic vector coherent states
• Influence of noncommutativity on the motion of Sun-Earth-Moon system and the weak equivalence principle
• Integral Transforms and $\mathcal{P}\mathcal{T}$-symmetric Hamiltonians
• Energy corrections due to the noncommutative phase-space of the charged isotropic harmonic oscillator in a uniform magnetic field in 3D
• Noncommutative quantum mechanics as a constrained system
• Quantum Theory of Tensionless Noncommutative p-Branes
• Fock Space Representations for Non-Hermitian Hamiltonians
• Dark Matter in a bi-metric universe
• Bohr-van Leeuwen theorem in non-commutative space
• Quantum dot with spin-orbit interaction in noncommutative phase space and analog Landau levels
• Two-dimensional Noncommutative atom Gas with Anandan interaction
• Inverse square problem and so(2,1) symmetry in noncommutative space
• Zitterbewegung in Noncommutative Geometry
• Emergent time crystals from phase-space noncommutative quantum mechanics
• Noncommutative effects in astrophysical objects: a survey
• Particle with spin 1 in a magnetic field on the spherical plane S_{2}
• Particle with spin 1 in a magnetic field on the hyperbolic plane H_{2}
• Lattice oscillator model on noncommutative space: eigenvalues problem for the perturbation theory
• Energy corrections due to the Non-commutative Phase-Space of the Charged Harmonic Oscillator in a constant magnetic field in 3D
• On a Dirac particle in an uniform magnetic field in 3-dimensional spaces of constant curvature
• Coupling constant of a noncommutative fermion
• Quantum mechanics for a vector particle in the magnetic field on 4-dimensional sphere
• Heisenberg quantization for the systems of identical particles and the Pauli exclusion principle in noncommutative spaces
• Schrödinger particle in magnetic and electric fields in Lobachevsky and Riemann spaces
• Electromagnetic Dualities on Noncommutative Space-Time and Symplectic Formalisms