Zeitschrift für Naturforschung A

Fractional Zero-Point Angular Momenta in Noncommutative Quantum Mechanics

Sijia Liu, Yufei Zhang, Zheng‐Wen Long, Jian Jing

Published Aug 24, 2016• 0 citations

Abstract

Abstract The charged particle confined by a harmonic potential in a noncommutative planar phase space interacting with a homogeneous dynamical magnetic field and Aharonov-Bohm potentials is studied. We find that the canonical orbital angular momenta of the reduced models, which are obtained by setting the mass and a dimensionless parameter to zero, take fractional values. These fractional angular momenta are not only determined by the flux inside the thin long solenoid but also affected by the noncommutativities of phase space.

DOI: 10.1515/zna-2016-0191

Related papers

Induced Fractional Zero-Point Canonical Angular Momentum on Charged Particles of Aharonov - Bohm Vector Potential and "Spectator" Magnetic Field

Jian-zu Zhang A B

The induced fractional zero-point canonical angular momentum on charged particles by the Aharonov - Bohm (AB) vector potential is realized via modified combined traps. It explores new features for this type of quantum effects: In a limit of vanishing mechanical kinetic energy the AB vector potential alone cannot induce a fractional zero-point canonical angular momentum on charged particles at the quantum mechanical level in the AB magnetic field-free region; But for the case of the AB vector potential with another one of a "spectator" magnetic field the AB vector potential induces a fractional zero-point canonical angular momentum in the same limit. The "spectator" one does not contribute to such a fractional zero-point quantity, but plays essential role in guaranteeing non-trivial dynamics survived in this limit at the quantum mechanical level. These results are significance in investigations of the AB effects and related fields for both theories and experiments.

arXiv:0709.0843Sep 6, 20070 citations

Aharonov–Bohm effect in noncommutative spaces

Масуд Чайчиан, Peter Prešnajder, Mohammad Mehdi Sheikh-Jabbari +1 more

The Aharonov–Bohm effect on the noncommutative plane is considered. Developing the path integral formulation of quantum mechanics, we find the propagation amplitude for a particle in a noncommutative space. We show that the corresponding shift in the phase of the particle propagator due to the magnetic field of a thin solenoid receives certain gauge invariant corrections because of the noncommutativity. Evaluating the numerical value for this correction, an upper bound for the noncommutativity parameter is obtained.

arXiv:hep-th/0012175Physics Letters BFeb 1, 2002171 citations

Induced fractional zero-point angular momentum for charged particles of the Bohm–Aharonov system by means of a “spectator” magnetic field

Jian-zu Zhang A B

An induced fractional zero-point angular momentum of charged particles by the Bohm–Aharonov (BA) vector potential is realized via a modified combined trap. It explores a “spectator” mechanism in this type of quantum effects: In the limit of the kinetic energy approaching one of its eigenvalues the BA vector potential alone cannot induce a fractional zero-point angular momentum at quantum mechanical level in the BA magnetic field-free region; But when there is a “spectator” magnetic field the BA vector potential induces a fractional zero-point angular momentum. The “spectator” does not contribute to such a fractional angular momentum, but plays essential role in guaranteeing non-trivial dynamics at quantum mechanical level in the required limit. This “spectator” mechanism is significant in investigating the BA effects and related topics in both aspects of theory and experiment.

arXiv:0901.2618Physics Letters BNov 8, 200810 citations

On the noncommutative Aharonov-Bohm effects

Jian Jing, Ling-Bao Kong, Qing xiang Wang +1 more

We revisit time-independent and time-dependent Aharonov-Bohm effects in the noncommutative space-time by investigating a relativistic spin-half particle in the background of a long-thin magnetic-flux-carried solenoid. Our results show that, up to the first order of the noncommutative parameter, there are no noncommutative corrections on the AB effects for both cases.

Physics Letters BAug 4, 202019 citations

The eigenvalues of the orbit angular momentum in noncommutative phase-space

Zhengren Zhang

In order to discuss the orbit angular momentum of the charged particle in noncommutative phase-space,the coordinate operators can be transformed into the annihilation and creation operators through a transformation matrix firstly.And then obtain the corresponding eigenvalues with the method of diagonalization.The result shows that there exists the zero-point angular momentum which is affected by the noncommutative parameters.

Yunnan Daxue xuebao. Shehui kexue banJan 1, 20110 citations

The fractional angular momentum realized by a cold neutral atom

Jian Jing, Qiu-Yue Zhang, Qing Wang +2 more

Inspired by the electromagnetic duality, we propose an approach to realize the fractional angular momentum by using a cold atom which possesses a permanent magnetic dipole momentum. This atom interacts with two electric fields and is trapped by a harmonic potential which enable the motion of the atom to be planar and rotationally symmetric. We show that eigenvalues of the canonical angular momentum of the cold atom can take fractional values when the atom is cooled down to its lowest kinetic energy level. The fractional part of canonical angular momentum is dual to that of the fractional angular momenta realized by using a charged particle. Another approach of getting the fractional angular momentum is also presented. The differences between these two approaches are investigated.

arXiv:1805.09854May 24, 20180 citations