Please wait a minute...
Chin. Phys. B, 2012, Vol. 21(4): 040303    DOI: 10.1088/1674-1056/21/4/040303
GENERAL Prev   Next  

Rotational symmetry of classical orbits, arbitrary quantization of angular momentum and the role of the gauge field in two-dimensional space

Xin Jun-Li(辛俊丽)a)b) and Liang Jiu-Qing(梁九卿)a)
a. Institute of Theoretical Physics, Shanxi University, Taiyuan 030006, China;
b. Department of Physics and Electronic Engineering, Yuncheng College, Yuncheng 044000, China
Abstract  We study quantum-classical correspondence in terms of the coherent wave functions of a charged particle in two-dimensional central-scalar potentials as well as the gauge field of a magnetic flux in the sense that the probability clouds of wave functions are well localized on classical orbits. For both closed and open classical orbits, the non-integer angular-momentum quantization with the level space of angular momentum being greater or less than  $\hbar$ is determined uniquely by the same rotational symmetry of classical orbits and probability clouds of coherent wave functions, which is not necessarily 2$\pi$-periodic. The gauge potential of a magnetic flux impenetrable to the particle cannot change the quantization rule but is able to shift the spectrum of canonical angular momentum by a flux-dependent value, which results in a common topological phase for all wave functions in the given model. The well-known quantum mechanical anyon model becomes a special case of the arbitrary quantization, where the classical orbits are 2$\pi$-periodic.
Keywords:  quantum-classical correspondence      anyon      rotational symmetry      arbitrary quantization of angular momentum  
Received:  22 June 2011      Revised:  10 October 2011      Accepted manuscript online: 
PACS:  03.65.Vf (Phases: geometric; dynamic or topological)  
  05.30.Pr (Fractional statistics systems)  
  45.20.df (Momentum conservation)  
  03.65.Ge (Solutions of wave equations: bound states)  
Fund: Project supported by the National Natural Science Foundation of China(Grant No.11075099)
Corresponding Authors:  Xin Jun-Li, E-mail:xinjunliycu@163.com     E-mail:  xinjunliycu@163.com

Cite this article: 

Xin Jun-Li(辛俊丽) and Liang Jiu-Qing(梁九卿) Rotational symmetry of classical orbits, arbitrary quantization of angular momentum and the role of the gauge field in two-dimensional space 2012 Chin. Phys. B 21 040303

[1] Makowski A J and Gorska K J 2007 J. Phys. A: Math. Theor. 40 11373
[2] Makowski A J and Gorska K J 2007 Phys. Lett. A 362 26
[3] Wilczek F 1982 Phys. Rev. Lett. 48 1144
[4] Wilczek F 1982 Phys. Rev. Lett. 49 957
[5] Plyushchay M S 1990 Phys. Lett. B 17 107
[6] Cortes J L and Plyushchay M S 1996 Int. J. Mod. Phys. A 11 3331
[7] Correa F and Plyushchay M S 2007 Ann. Phys. 322 2493
[8] Correa F, Falomir H, Jakubsky V and Plyushchay M S 2010 J. Phys. A: Math. Theor. 43 075202
[9] Correa F, Falomir H, Jakubsky V and Plyushchay M S 2010 Ann. Phys. 325 2653
[10] Jakubsky V, Nieto Luis-Miguel and Plyushchay M S 2010 Phys. Lett. B 692 51
[11] Horvathy P A, Plyushchay M S and Valenzuela M 2010 Ann. Phys. 325 1931
[12] Ding X X and Liang J Q 1988 Acta Phys. Sin. 37 1752 (in Chinese)
[13] Silverman M 1983 Phys. Rev. Lett. 17 1927
[14] Hamermesh M 1962 Group Theory and Its Applications to Physical Problems (Reading MA: Addison Wesley Publishing Company)
[15] Liang J Q 1984 Phys. Rev. Lett. 53 859
[16] Schulman L 1968 Phys. Rev. A 176 1558
[17] Jackiw R and Redlich A M 1983 Phys. Rev. Lett. 50 555
[18] Liang J Q and Ding X X 1987 Phys. Rev. A 36 4149
[19] Makowski A J 2002 Phys. Rev. A 65 32103
[20] Makowski A J and Gorska K J 2002 Phys. Rev. A 66 062103
[21] Wang H, Wang X T, Gould P L and Stwalley W C 1997 Phys. Rev. Lett. 78 4173
[22] Makowski A J 2003 Phys. Rev. A 68 22102
[23] Kobayashi T 2002 Physica A 303 469
[24] Nowakowski M and Rosu H C 2002 Phys. Rev. E 65 047602
[25] Makowski A J 2005 J. Phys. A: Math. Gen. 17 2299
[26] Daboul J and Nieto M M 1995 Phys. Rev. E 52 4430
[27] Makowski A J 2010 Ann. Phys. 325 1622
[28] Daboul J and Nieto M M 1996 Int. J. Mod. Phys. A 11 3801
[29] Daboul J and Nieto M M 1994 Phys. Lett. A 190 357
[30] Watson G N 1952 Theory of Bessel Function (Lodon: Cambrige University Press)
[31] Klauder J R and Skagerstam Bo-Sture 1986 Coherehent States-Applications in Physics and Mathematical Physics (Singapore: World Scientific)
[32] Tian L J, Zhu C Q, Zhang H B and Qin L G 2011 Chin. Phys. B 20 040302
[33] Lai Y Z and Liang J Q 1996 Acta Phys. Sin. 45 738 (in Chinese)
[34] Leinaas J M and Myrheim J 1988 Phys. Rev. B 37 9286
[35] He Y J, Fab H H, Dong J W and Wang H Z 2006 Phys. Rev. E 74 016611
[36] Desyatnikov A S and Kivshar Y S 2001 Phys. Rev. Lett. 87 033901
[37] Goryo J 2000 Phys. Rev. B 31 4222
[38] Gongora T A, Jose J V, Schaffner S and Tiesinga P H E 2000 Phys. Lett. A 274 117
[1] Entanglement spectrum of non-Abelian anyons
Ying-Hai Wu(吴英海). Chin. Phys. B, 2022, 31(3): 037302.
[2] Simulation of anyons by cold atoms with induced electric dipole moment
Jian Jing(荆坚), Yao-Yao Ma(马瑶瑶), Qiu-Yue Zhang(张秋月), Qing Wang(王青), Shi-Hai Dong(董世海). Chin. Phys. B, 2020, 29(8): 080303.
[3] Chaotic dynamics of complex trajectory and its quantum signature
Wen-Lei Zhao(赵文垒), Pengkai Gong(巩膨恺), Jiaozi Wang(王骄子), and Qian Wang(王骞). Chin. Phys. B, 2020, 29(12): 120302.
[4] Entangled multi-knot lattice model of anyon current
Tieyan Si(司铁岩). Chin. Phys. B, 2019, 28(4): 040501.
No Suggested Reading articles found!