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Frontiers of Physics

Quantum phase for an electric quadrupole moment in noncommutative quantum mechanics

Halqem Nizamidin, Abduwali Anwar, Sayipjamal Dulat A, Kang Li B

Published May 8, 2014• 16 citations
Publisher

Abstract

We study the noncommutative nonrelativistic quantum dynamics of a neutral particle, which possesses an electric qaudrupole moment, in the presence of an external magnetic field. First, by introducing a shift for the magnetic field, we give the Schrödinger equations in the presence of an external magnetic field both on a noncommutative space and a noncommutative phase space, respectively. Then by solving the Schrödinger equations both on a noncommutative space and a noncommutative phase space, we obtain quantum phases of the electric quadrupole moment, respectively. We demonstrate that these phases are geometric and dispersive.

DOI
10.1007/s11467-014-0425-1

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We study the noncommutative nonrelativistic quantum dynamics of a neutral particle, which possesses an electric qaudrupole moment, in the presence of an external magnetic field. First, by introducing a shift for the magnetic field, we give the Schrödinger equations in the presence of an external magnetic field both on a noncommutative space and a noncommutative phase space, respectively. Then by solving the Schrödinger equations both on a noncommutative space and a noncommutative phase space, we obtain quantum phases of the electric quadrupole moment, respectively. We demonstrate that these phases are geometric and dispersive.
In this work, we study the noncommutative nonrelativistic quantum dynamics of a neutral particle, which possesses permanent magnetic and electric dipole moments, in the presence of external electric and magnetic fields. We use the Foldy-Wouthuysen transformation of the Dirac spinor with a nonminimal coupling to obtain the nonrelativistic limit. In this limit, we study the noncommutative quantum dynamics and obtain the noncommutative Anandan geometric phase. We analyze the situation where the 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 by considering the noncommutativity in the phase space, and the Anandan phase is obtained.
The dynamics of a spin-(1/2) neutral particle possessing electric- and magnetic-dipole moments interacting with external electric and magnetic fields in noncommutative coordinates is obtained. Noncommutativity of space is interposed in terms of a semiclassical constrained Hamiltonian system. The relation between the quantum phase acquired by a particle interacting with an electromagnetic field and the (semi)classical force acting on the system is examined and generalized to establish a formulation of the quantum phases in noncommutative coordinates. The general formalism is applied to physical systems yielding the Aharonov-Bohm, Aharonov-Casher, He-McKellar-Wilkens and Anandan phases in noncommutative coordinates. Bounds for the noncommutativity parameter θ are derived comparing the deformed phases with the experimental data on the Aharonov-Bohm and Aharonov-Casher phases.
The Aharonov-Bohm (AB) effect in non-commutative quantum mechanics (NCQM) is studied. First, by introducing a shift for the magnetic vector potential we give the Schrddoto\\ddot{o}ddotodinger equations in the presence of a magnetic field on NC space and NC phase space, respectively. Then by solving the Schrddoto\\ddot{o}ddotodinger equations, we obtain the Aharonov-Bohm (AB) phase on NC space and NC phase space, respectively.