Hall Effect in Noncommutative Coordinates
arXiv:hep-th/0111267 · doi:10.1063/1.1504484
Abstract
We consider electrons in uniform external magnetic and electric fields which move on a plane whose coordinates are noncommuting. Spectrum and eigenfunctions of the related Hamiltonian are obtained. We derive the electric current whose expectation value gives the Hall effect in terms of an effective magnetic field. We present a receipt to find the action which can be utilized in path integrals for noncommuting coordinates. In terms of this action we calculate the related Aharonov--Bohm phase and show that it also yields the same effective magnetic field. When magnetic field is strong enough this phase becomes independent of magnetic field. Measurement of it may give some hints on spatial noncommutativity. The noncommutativity parameter θcan be tuned such that electrons moving in noncommutative coordinates are interpreted as either leading to the fractional quantum Hall effect or composite fermions in the usual coordinates.
13 pages. Some references added
References in corpus (7)
- The Landau problem and noncommutative quantum mechanics
- Quantum Theories on Noncommutative Spaces with Nontrivial Topology: Aharonov-Bohm and Casimir Effects
- Physical Instances of Noncommuting Coordinates
- Orbital Magnetism of Two-Dimension Noncommutative Confined System
- Landau Diamagnetism in Noncommutative Space and the Nonextensive Thermodynamics of Tsallis
- Noncommutative Quantum Mechanics and rotating frames
- Noncommutativity and the Aharonov-Bohm Effect
Cited by in corpus (69)
- The topological AC effect on noncommutative phase space
- Dual families of non-commutative quantum systems
- The HMW effect in Noncommutative Quantum Mechanics
- On noncommutative isotropic harmonic oscillator
- Interactions and non-commutativity in quantum Hall systems
- Twisted Galilean symmetry and the Pauli principle at low energies
- An Analogy of the Quantum Hall Condutivity in a Lorentz-symmetry Violation Setup
- Magnetic fields in noncommutative quantum mechanics
- Noncommutative Quantum Mechanics and Seiberg-Witten Map
- The Noncommutative Anandan's Quantum Phase
- Noncommutative Quantum Hall Effect and Aharonov-Bohm Effect
- Landau Problem in Noncommutative Quantum Mechanics
- Gauge Covariance of the Aharonov-Bohm Phase in Noncommutative Quantum Mechanics
- Landau Analog Levels for Dipoles in the Noncommutative Space and Phase Space
- Harmonic Superspace Gaugeon Formalism for the ABJM Theory
- Quantum Hall Effect In Bilayer Systems And The Noncommutative Plane: A Toy Model Approach
- Spin Hall effect on a noncommutative space
- Inertial spin Hall effect in noncommutative space
- The noncommutative quantum Hall effect with anomalous magnetic moment in three different relativistic scenarios
- A Noncommutative Space Approach to Confined Dirac Fermions in Graphene
- A Deformation Quantization Theory for Non-Commutative Quantum Mechanics
- Schwinger Model In Noncommutating Space-Time
- The non-commutative and discrete spatial structure of a 3D Wigner quantum oscillator
- 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
- The BV Formalization of Chern-Simons Theory on Deformed Superspace
- The Aharonov-Casher effect for spin-1 particles in non-commutative quantum mechanics
- Harmonic oscillator chains as Wigner Quantum Systems: periodic and fixed wall boundary conditions in gl(1|n) solutions
- Angular momentum quantum backflow in the noncommutative plane
- Worldline approach to noncommutative field theory
- Non-anticommutative ABJ Theory
- Spin Hall Effect in Noncommutative Coordinates
- Path Integrals in Noncommutative Quantum Mechanics
- Twist Deformation of Rotationally Invariant Quantum Mechanics
- Non-commutativity and non-inertial effects on a scalar field in a cosmic string space-time. Part 1: Klein-Gordon oscillator
- Berry's phase in noncommutative spaces
- Relativistic and nonrelativistic Landau levels for the noncommutative quantum Hall effect with anomalous magnetic moment in a conical Gödel-type spacetime
- Exact solutions of a damped harmonic oscillator in a time dependent noncommutative space
- Dynamics of Dipoles and Quantum Phases in Noncommutative Coordinates
- Exact solution of damped harmonic oscillator with a magnetic field in a time dependent noncommutative space
- Effects of Twisted Noncommutativity in Multi-particle Hamiltonians
- Non-Commutativity effects in the Dirac equation in crossed electric and magnetic fields
- Analogue of the quantum Hall effect for neutral particles with magnetic dipole moment
- Gauge invariant energy spectra in 2-dimensional noncommutative quantum mechanics
- An Alternative Formulation of Hall Effect and Quantum Phases in Noncommutative Space
- Landau levels in a 2D noncommutative space: matrix and quaternionic vector coherent states
- Noncommutativity Parameter and Composite Fermions
- Energy corrections due to the noncommutative phase-space of the charged isotropic harmonic oscillator in a uniform magnetic field in 3D
- Voros product and the Pauli principle at low energies
- Measuring Space Deformation via Graphene under Constraints
- Bohr-van Leeuwen theorem in non-commutative space
- Noncommutative Landau problem in graphene: a gauge-invariant analysis with the Seiberg-Witten map
- On a charged spinless point particle minimally coupled to a constant magnetic field in a noncommutative plane
- Coherent states for a system of an electron moving on plane
- Electromagnetism in terms of quantum measurements
- Quantum dot with spin-orbit interaction in noncommutative phase space and analog Landau levels
- Backward Compton Scattering and QED with Noncommutative Plane in the Strong Uniform Magnetic Field
- On plane wave and vortex-like solutions of noncommutative Maxwell-Chern-Simons theory
- Quantum harmonic oscillator in a time dependent noncommutative background
- Dirac equation with a magnetic field in 3D non-commutative phase space
- Two-dimensional Noncommutative atom Gas with Anandan interaction
- Symplectic Fluctuations for Electromagnetic Excitations of Hall Droplets
- Second Virial Coefficient for Noncommutative Space
- Thermodynamical Properties of Hall Systems
- Inverse square problem and so(2,1) symmetry in noncommutative space
- Thermodynamics Properties of Confined Particles on Noncommutative Plane
- Charged Dirac fermions with anomalous magnetic moment in the presence of the chiral magnetic effect and of a noncommutative phase space
- Pauli energy spectrum for twist-deformed space-time
- Dynamic and static properties of Quantum Hall and Harmonic Oscillator systems on the non-commutative plane
- Lattice oscillator model on noncommutative space: eigenvalues problem for the perturbation theory