1. School of Mathematical Science, Capital Normal University, Beijing 100048, China 2. School of Physics Science and Technology, Xinjiang University, Urumqi 830046, China 3. Department of Physics, Hangzhou Normal University, Hangzhou 310036, China
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 Schr?dinger equations in the presence of an external magnetic field both on a noncommutative space and a noncommutative phase space, respectively. Then by solving the Schr?dinger 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.
. [J]. Frontiers of Physics, 2014, 9(4): 446-450.
Halqem Nizamidin,Abduwali Anwar,Sayipjamal Dulat,Kang Li. Quantum phase for an electric quadrupole moment in noncommutative quantum mechanics. Front. Phys. , 2014, 9(4): 446-450.
S. Godfrey and M. A. Doncheski, Signals for noncommutative QED in eγ and γγ collisions, Phys. Rev. D, 2001, 65(1): 015005 doi: 10.1103/PhysRevD.65.015005
2
M. Haghighat and M. M. Ettefaghi, Parton model in Lorentz invariant noncommutative space, Phys. Rev. D, 2004, 70(3): 034017 doi: 10.1103/PhysRevD.70.034017
3
A. Devoto, S. Chiara, and W. W. Repko, Noncommutative QED corrections to e+e-→γγγ at linear collider energies, Phys. Rev. D, 2005, 72(5): 056006 doi: 10.1103/PhysRevD.72.056006
4
X. Calmet, Quantum electrodynamics on noncommutative spacetime, Eur. Phys. J. C, 2007, 50(1): 113 doi: 10.1140/epjc/s10052-006-0192-4
5
M. Chaichian, A. Demichev, P. Pre?najder, M. M. Sheikh-Jabbari, and A. Tureanu, Aharonov–Bohm effect in noncommutative spaces, Phys. Lett. B, 2002, 527(1-2): 149 doi: 10.1016/S0370-2693(02)01176-0
6
M. Chaichian, A. Demichev, P. Presnajder, M. M. Sheikh-Jabbari, and A. Tureanu, Quantum theories on noncommutative spaces with nontrivial topology: Aharonov–Bohm and Casimir effects, Nucl. Phys. B, 2001, 611(1-3): 383 doi: 10.1016/S0550-3213(01)00348-0
7
H. Falomir, J. Gamboa, M. Loewe, F. Méndez, and J. Rojas, Testing spatial noncommutativity via the Aharonov–Bohm effect, Phys. Rev. D, 2002, 66(4): 045018 doi: 10.1103/PhysRevD.66.045018
8
K. Li and S. Dulat, The Aharonov–Bohm effect in noncommutative quantum mechanics, Eur. Phys. J. C, 2006, 46(3): 825 doi: 10.1140/epjc/s2006-02538-2
9
B. Mirza and M. Zarei, Non-commutative quantum mechanics and the Aharonov–Casher effect, Eur. Phys. J. C, 2004, 32(4): 583 doi: 10.1140/epjc/s2003-01522-8
10
K. Li and J. H. Wang, The topological AC effect on noncommutative phase space, Eur. Phys. J. C, 2007, 50(4): 1007 doi: 10.1140/epjc/s10052-007-0256-0
11
B. Mirza, R. Narimani, and M. Zarei, Aharonov–Casher effect for spin-1 particles in a non-commutative space, Eur. Phys. J. C, 2006, 48(2): 641 doi: 10.1140/epjc/s10052-006-0047-z
12
S. Dulat and K. Li, The Aharonov–Casher effect for spin-1 particles in non-commutative quantum mechanics, Eur. Phys. J. C, 2008, 54(2): 333 doi: 10.1140/epjc/s10052-008-0522-9
13
S. Dulat, K. Li, and J. Wang, The He–McKellar–Wilkens effect for spin one particles in non-commutative quantum mechanics, J. Phys. A: Math. Theor., 2008, 41(6): 065303 doi: 10.1088/1751-8113/41/6/065303
14
B. Harms and O. Micu, Noncommutative quantum Hall effect and Aharonov–Bohm effect, J. Phys. A, 2007, 40(33): 10337 doi: 10.1088/1751-8113/40/33/024
15
O. F. Dayi and A. Jellal, Hall effect in noncommutative coordinates, J. Math. Phys., 2002, 43(10): 4592 doi: 10.1063/1.1504484
16
O. F. Dayi and A. Jellal, Erratum: “Hall effect in noncommutative coordinates” [J. Math. Phys. 43, 4592 (2002)], J. Math. Phys., 2004, 45(2): 827 (E) doi: 10.1063/1.1636511
17
A. Kokado, T. Okamura, and T. Saito, Noncommutative phase space and the Hall effect, Prog. Theor. Phys., 2003, 110(5): 975 doi: 10.1143/PTP.110.975
18
S. Dulat and K. Li, Quantum Hall effect in noncommutative quantum mechanics, Eur. Phys. J. C, 2009, 60(1): 163 doi: 10.1140/epjc/s10052-009-0886-5
19
B. Chakraborty, S. Gangopadhyay, and A. Saha, Seiberg–Witten map and Galilean symmetry violation in a noncommutative planar system, Phys. Rev. D, 2004, 70(10): 107707arXiv: hep-th/0312292 doi: 10.1103/PhysRevD.70.107707
20
F. G. Scholtz, B. Chakraborty, S. Gangopadhyay, and A. G. Hazra, Dual families of noncommutative quantum systems, Phys. Rev. D, 2005, 71(8): 085005 doi: 10.1103/PhysRevD.71.085005
21
F. G. Scholtz, B. Chakraborty, S. Gangopadhyay, and J. Govaerts, Interactions and non-commutativity in quantum Hall systems, J. Phys. A, 2005, 38(45): 9849 doi: 10.1088/0305-4470/38/45/008
22
?. F. Dayi and M. Elbistan, Spin Hall effect in noncommutative coordinates, Phys. Lett. A, 2009, 373(15): 1314 doi: 10.1016/j.physleta.2009.02.029
23
K. Ma and S. Dulat, Spin Hall effect on a noncommutative space, Phys. Rev. A, 2011, 84(1): 012104 doi: 10.1103/PhysRevA.84.012104
24
E. Passos, L. R. Ribeiro, C. Furtado, and J. R. Nascimento, Noncommutative Anandan quantum phase, Phys. Rev. A, 2007, 76(1): 012113 doi: 10.1103/PhysRevA.76.012113
25
C. C.Chen, Topological quantum phase and multipole moment of neutral particles, Phys. Rev. A, 1995, 51(3): 2611 doi: 10.1103/PhysRevA.51.2611
26
T. Curtright, D. Fairlie, and C. Zachos, Features of timeindependent Wigner functions, Phys. Rev. D, 1998, 58(2): 025002 doi: 10.1103/PhysRevD.58.025002
