© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:1107.5636 · Physical Review A

Two-dimensional noncommutative atom gas with the Anandan interaction

Yu Xiao-Min, Kang Li B

Published Sep 14, 2011• 2 citations

Abstract

Landau-like quantization of the Anandan system in a special electromagnetic field is studied. Unlike the cases of the Aharonov-Casher (AC) system and the He-McKellar-Wilkens (HMW) system, the torques of the system on the magnetic dipole and the electric dipole do not vanish. By constructing Heisenberg algebra, the Landau analog levels and eigenstates on commutative space, noncommutative (NC) space, and NC phase space are obtained, respectively. By using the coherent state method, some statistical properties of such free-atom gas are studied and the expressions of some thermodynamic quantities related to revolution direction are obtained. Two particular cases of temperature are discussed and the more simple expressions of the free energy on the three spaces are obtained. We give the relation between the value of $\ensuremath{\sigma}$ and revolution direction clearly and find Landau like levels of the Anandan system are invariant and the levels between the AC system and the HMW system are interchanged each other under Maxwell dual transformations on the three spaces. The two sets of eigenstates labeled by $\ensuremath{\sigma}$ can be related by a supersymmetry transformation on commutative space, but the phenomenon do not occur on NC situation. We emphasize that some results relevant to Anandan interaction are suitable for the cases of AC interaction and HMW interaction under special conditions.

DOI: 10.1103/physreva.84.033617

Related papers

Noncommutative (2+1)-dimensional Anandan effects

Jian Jing, Yali Wang, Qing Wang +2 more

By identifying the model of a relativistic spin-half neutral particle which possesses magnetic and electric dipole moments interacting with an electromagnetic field as the [Formula: see text] gauge theory, we study the Anandan phase in [Formula: see text]-dimensional noncommutative space–time by applying the Seiberg–Witten map. We find that up to the first order of the noncommutative parameter, Anandan phase does not receive any corrections due to the spatial noncommutativity. Our result also indicates that phases of either Aharonov–Casher or He–Mckellar–Wilkens effects can receive corrections due to spatial noncommutativity.

International Journal of Modern Physics A•Sep 25, 2022•4 citations

Dynamics of dipoles and quantum phases in noncommutative coordinates

Ö. F. Dayi

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.

arXiv:0810.5468•Europhysics Letters (EPL)•Feb 1, 2009•9 citations

Anandan Quantum Phase of Spin-1/2 Particles

Li Kang

By solving the Dirac function,the paper obtained the phase changes of the wave function in non-commutative space and non-commutative phase space when a neutral spin-1/2 particle with nonzero magnetic and electric dipoles moved in an external electromagnetic field,and discussed the related Aharonov-Casher effect and the He-McKellar-Wilkens effect.

Journal of Hangzhou Teachers College•Jan 1, 2011•0 citations

Solution of the Dipoles in Noncommutative Space with Minimal Length*

Meng-Yao Zhang, Zheng‐Wen Long, Chao‐Yun Long

Abstract The single neutral spin-half particle with electric dipole moment and magnetic dipole moment moving in an external electromagnetic field is studied. The Aharonov-Casher effect and He-McKellar-Wilkens effect are emphatically discussed in noncommutative (NC) space with minimal length. The energy eigenvalues of the systems are obtained exactly in terms of the Jacobi polynomials. Additionally, a special case is discussed and the related energy spectra are plotted.

Communications in Theoretical Physics•Jun 1, 2019•3 citations

Noncommutative Anandan quantum phase

Eduardo Passos, L. R. Ribeiro, Claudio Furtado +1 more

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.

arXiv:hep-th/0610222•Physical Review A•Jul 18, 2007•50 citations

Magnetic oscillations for neutral atoms subject to an electromagnetic field

B. Farias, Claudio Furtado

We show that the de Haas van Alphen effect can be induced in a two dimensional atomic gas by the He-McKellar-Wilkens interaction mediated via an electric dipole moment. Under an appropriate field-dipole configuration, we show that the neutral atoms subject to a synthetic magnetic field arrange themselves in Landau levels. An experimental arrangement for observation of the atomic analog of dHvA oscillations is proposed. In a strong effective magnetic field regime we present the quantum oscillations in the energy and effective magnetization of the two dimensional atomic gas. From the dHvA period we determine the area of the Fermi circle of the atomic cloud.

arXiv:1708.00332•Jul 30, 2017•0 citations

Landau-like quantization of the Anandan system in a special electromagnetic field is studied. Unlike the cases of the Aharonov-Casher (AC) system and the He-McKellar-Wilkens (HMW) system, the torques of the system on the magnetic dipole and the electric dipole do not vanish. By constructing Heisenberg algebra, the Landau analog levels and eigenstates on commutative space, noncommutative (NC) space, and NC phase space are obtained, respectively. By using the coherent state method, some statistical properties of such free-atom gas are studied and the expressions of some thermodynamic quantities related to revolution direction are obtained. Two particular cases of temperature are discussed and the more simple expressions of the free energy on the three spaces are obtained. We give the relation between the value of

\ensuremath{\sigma}

and revolution direction clearly and find Landau like levels of the Anandan system are invariant and the levels between the AC system and the HMW system are interchanged each other under Maxwell dual transformations on the three spaces. The two sets of eigenstates labeled by

\ensuremath{\sigma}

can be related by a supersymmetry transformation on commutative space, but the phenomenon do not occur on NC situation. We emphasize that some results relevant to Anandan interaction are suitable for the cases of AC interaction and HMW interaction under special conditions.

By identifying the model of a relativistic spin-half neutral particle which possesses magnetic and electric dipole moments interacting with an electromagnetic field as the [Formula: see text] gauge theory, we study the Anandan phase in [Formula: see text]-dimensional noncommutative space–time by applying the Seiberg–Witten map. We find that up to the first order of the noncommutative parameter, Anandan phase does not receive any corrections due to the spatial noncommutativity. Our result also indicates that phases of either Aharonov–Casher or He–Mckellar–Wilkens effects can receive corrections due to spatial noncommutativity.

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.

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.

We show that the de Haas van Alphen effect can be induced in a two dimensional atomic gas by the He-McKellar-Wilkens interaction mediated via an electric dipole moment. Under an appropriate field-dipole configuration, we show that the neutral atoms subject to a synthetic magnetic field arrange themselves in Landau levels. An experimental arrangement for observation of the atomic analog of dHvA oscillations is proposed. In a strong effective magnetic field regime we present the quantum oscillations in the energy and effective magnetization of the two dimensional atomic gas. From the dHvA period we determine the area of the Fermi circle of the atomic cloud.