The Noncommutative Anandan's Quantum Phase

Abstract

In this work we study the noncommutative nonrelativistic quantum dynamics of a neutral particle, that possesses permanent magnetic and electric dipole momenta, in the presence of an electric and magnetic fields. We use the Foldy-Wouthuysen transformation of the Dirac spinor with a non-minimal coupling to obtain the nonrelativistic limit. In this limit, we will study the noncommutative quantum dynamics and obtain the noncommutative Anandan's geometric phase. We analyze the situation where magnetic dipole moment of the particle is zero and we obtain the noncommutative version of the He-McKellar-Wilkens effect. We demonstrate that this phase in the noncommutative case is a geometric dispersive phase. We also investigate this geometric phase considering the noncommutativity in the phase space and the Anandan's phase is obtained.

15 pages, revtex4, version to appear in Physical Review A

References in corpus (23)

• String Theory and Noncommutative Geometry
• Noncommutative Field Theory
• Noncommutative Geometry and Matrix Theory: Compactification on Tori
• Hydrogen Atom Spectrum and the Lamb Shift in Noncommutative QED
• Quantum mechanics on the noncommutative plane and sphere
• Features of Time-independent Wigner Functions
• Topological phase due to electric dipole moment and magnetic monopole interaction
• Aharonov-Bohm Effect in Noncommutative Spaces
• Quantum Theories on Noncommutative Spaces with Nontrivial Topology: Aharonov-Bohm and Casimir Effects
• Fractional Angular Momentum in Noncommutative Space
• Hall Effect in Noncommutative Coordinates
• Classical and Quantum Interaction of the Dipole
• Testing spatial noncommutativiy via the Aharonov-Bohm effect
• The topological AC effect on noncommutative phase space
• The Aharonov-Bohm Effect in Noncommutative Quantum Mechanics
• Topology, Locality, and Aharonov-Bohm Effect with Neutrons
• Noncommutative quantum mechanics and the Aharonov-Casher effect
• Representation of noncommutative phase space
• Quantum Dynamics of Magnetic and Electric Dipoles and Berry's Phase
• Quantum Mechanics on Noncommutative Spacetime
• Quantum Hall Effect In Bilayer Systems And The Noncommutative Plane: A Toy Model Approach
• Noncommutative Geometry and Geometric Phases
• Berry's phase in noncommutative spaces

Cited by in corpus (22)

• On the interaction of the Dirac oscillator with the Aharonov-Casher system in topological defect backgrounds
• Landau quantization for a neutral particle in presence of topological defects
• Geometric Phase for Neutral Particle in the Presence of a Topological Defect
• Relativistic Landau-Aharonov-Casher quantization based on the Lorentz symmetry violation background
• Relativistic Landau quantization for a neutral particle
• He-McKellar-Wilkens effect and Scalar Aharonov-Bohm effect for a neutral particle based on the Lorentz symmetry violation
• Gravitational Geometric Phase in the Presence of Torsion
• Landau Analog Levels for Dipoles in the Noncommutative Space and Phase Space
• Quantum Holonomies based on the Lorentz-violating tensor background
• The noncommutative quantum Hall effect with anomalous magnetic moment in three different relativistic scenarios
• On Aharonov-Casher bound states
• A geometric approach to confining a Dirac neutral particle in analogous way to a quantum dot
• Relativistic geometric quantum phases from the Lorentz symmetry violation effects in the CPT-even gauge sector of Standard Model Extension
• An angular frequency dependence on the Aharonov-Casher geometric phase
• 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
• Quantum effects of Aharonov-Bohm type and noncommutative quantum mechanics
• On atomic analogue of Landau quantization
• Dynamics of Dipoles and Quantum Phases in Noncommutative Coordinates
• An Alternative Formulation of Hall Effect and Quantum Phases in Noncommutative Space
• Two-dimensional Noncommutative atom Gas with Anandan interaction
• Induced electric dipole moment coupling in Dirac equation