Exact solutions of a spin-orbit coupling model in two-dimensional central-potentials and quantum-classical correspondence

详细信息    查看全文

• 作者：JunLi Xin (1) (2)
  JiuQing Liang (1)
  
• 关键词：spin ; orbit coupling ; non ; Abelian gauge field ; quantum ; classical correspondence ; fractional quantization of orbital angular ; momentum
• 刊名：SCIENCE CHINA Physics, Mechanics & Astronomy
• 出版年：2014
• 出版时间：August 2014
• 年：2014
• 卷：57
• 期：8
• 页码：1504-1510
• 全文大小：679 KB
• 参考文献：1. Chen Y F. Geometry of classical periodic orbits and quantum coherent states in coupled oscillators with SU(2) transformations. Phys Rev A, 2011, 83: 032124 CrossRef
  2. Nieto M M, Daboul J. Exact, / E = 0, classical solutions for general power-law potentials. Phys Rev E, 1995, 52: 4430鈥?441; Daboul J, Nieto M M. / E = 0, quantum solutions for general power-law potentials. Int J Mod Phys A, 1996, 11: 3801鈥?817 CrossRef
  3. Makowski A J, Gorska K J. Fractional and integer angular momentum wavefunctions localized on classical orbits: The case of / E = 0. J Phys A-Math Theory, 2007, 40: 11373鈥?1383 CrossRef
  4. Makowski A J, Gorska K J. Quantization of the Maxwell fish-eye problem and the quantum-classical correspondence. Phys Rev A, 2009, 79: 052116 CrossRef
  5. Graefe E M, Korsch H J, Niederle A E. Quantum-classical correspondence for a non-Hermitian Bose-Hubbard dimer. Phys Rev A, 2010, 82: 013629 CrossRef
  6. Brack M. The physics of simple metal clusters: Self-consistent jellium model and semiclassical approaches. Rev Mod Phys, 1993, 65: 677鈥?32 CrossRef
  7. de Heer W A. The physics of simple metal clusters: Experimental aspects and simple models. Rev Mod Phys, 1993, 65: 611鈥?76 CrossRef
  8. Zozoulenko I V, Berggren K F. Quantum scattering, resonant states, and conductance fluctuations in an open square electron billiard. Phys Rev B, 1997, 56: 6931鈥?941 CrossRef
  9. Brunner R, Meisels R, Kuchar F, et al. Draining of the sea of chaos: Role of resonant transmission and reflection in an array of billiards. Phys Rev Lett, 2007, 98: 204101 CrossRef
  10. Peters A D, Jaff茅 C, Delos J B. Quantum manifestations of bifurcations of classical orbits: An exactly solvable model. Phys Revs Lett, 1994, 73: 2825鈥?828 CrossRef
  11. Bracher C, Delos J B. Motion of an electron from a point source in parallel electric and magnetic fields. Phys Rev Lett, 2006, 96: 100404 CrossRef
  12. Makowski A J. Quantum-classical correspondence for motion on a plane with deficit angle. Ann Phys, 2010, 325: 1622鈥?632 CrossRef
  13. Sadeghpour H R, Bohn J L, Cavagnero M J, et al. Collisions near threshold in atomic and molecular physics. J Phys B-At Mol Opt Phys, 2000, 33: R93鈥揜140 CrossRef
  14. Wang H, Wang X T, Gould P L, et al. Optical-optical double resonance photoassociative spectroscopy of ultracold 39 K atoms near highly excited asymptotes. Phys Rev Lett, 1997, 78: 4173鈥?176 CrossRef
  15. Kobayashi T. Vortex lattices in quantum mechanics. Phys A, 2002, 303: 469鈥?80 CrossRef
  16. Schr枚dinger E. Der stetige 眉bergang von der Mikro-zur Makromechanik. Naturwissenschaften, 1926, 14: 664鈥?66 CrossRef
  17. Zhang W M, Feng D H, Gilmore R. Coherent states: Theory and some applications. Rev Mod Phys, 1990, 62: 867鈥?27 CrossRef
  18. Klauder J R, Sture S B. Coherent States-Applications in Physics and Mathematical Physics. Singapore: World Scientific, 1985 CrossRef
  19. Muminov Kh Kh, Yousefi Y. Coherent states in real parameterization up to SU(5) and classical dynamics of spin systems. arXiv:1103.6080
  20. Zurek W H, Habib S, Paz J P. Coherent states via decoherence. Phys Rev Lett, 1993, 70: 1187鈥?190 CrossRef
  21. Murakami S, Nagaosa N, Zhang S C, et al. Dissipationless quantum spin current at room temperature. Science, 2003, 301: 1348鈥?351; Sinova J, Culcer D, Niu Q, et al. Universal intrinsic spin Hall effect. Phys Rev Lett, 2004, 92: 126603 CrossRef
  22. Kato Y K, Myers R C, Gossard A C, et al. Observation of the spin Hall Effect in semiconductors. Science, 2004, 306: 1910鈥?913; Wunderlich J, Kaestner B, Sinova J, et al. Experimental observation of the spin-Hall effect in a two-dimensional spin-orbit coupled semiconductor system. Phys Rev Lett, 2005, 94: 047204 CrossRef
  23. Ho T L, Zhang S Z. Bose-Einstein condensates in non-Abelian gauge fields. arXiv:1007.0650
  24. Lin Y J, Jim茅nez-Garc铆a K, Spielman I B. Spin-orbit-coupled Bose-Einstein condensates. Nature, 2011, 471: 83鈥?6 CrossRef
  25. Yip S K. Bose-Einstein condensation in the presence of an artificial spin-orbit interaction. arXiv:1008.2263
  26. Wolf S A, Awschalom D D, Buhrman R A, et al. Spintronics: A spinbased electronics vision for the future. Science, 2001, 294: 1488鈥?495 CrossRef
  27. Abiague A M, Fabian J. Anisotropic tunneling magnetoresistance and tunneling anisotropic magnetoresistance: Spin-orbit coupling in magnetic tunnel junctions. Phys Rev B, 2009, 79: 155303 CrossRef
  28. Jacob A, 脰hberg P, Juzeli奴nas G, et al. Cold atom dynamics in non-Abelian gauge fields. Appl Phys B, 2007, 89: 439鈥?45 CrossRef
  29. Wilczek F, Zee A. Appearance of gauge structure in simple dynamical systems. Phys Rev Lett, 1984, 52: 2111鈥?114 CrossRef
  30. Dum R, Olshanii M. Gauge structures in atom-laser interaction: Bloch oscillations in a dark lattice. Phys Rev Lett, 1996, 76: 1788鈥?791; Lin Y J, Compton R L, Perry A R, et al. Bose-Einstein condensate in a uniform light-induced vector potential, Phys Rev Lett, 2009, 102: 130401 CrossRef
  31. Larson J, Levin S. Effective Abelian and non-Abelian gauge potentials in cavity QED. Phys Rev Lett, 2009, 103: 013602 CrossRef
  32. Balachandran A P, Marmo G, Skagerstam B S, et al. Gauge Symmetries and Fibre Bundels. Berlin: Springer Verlag, 1983
  33. Aharonov Y, Casher A. Topological quantum effects for neutral particles. Phys Rev Lett, 1984, 53: 319鈥?21 CrossRef
  34. Liang J Q, Ding X X. Dynamics of a neutron in electromagnetic fields and quantum phase interference. Phys Lett A, 1993, 176: 165鈥?72 CrossRef
  35. Liang J Q, Marmo G, Simoni A, et al. Dynamics in two-dimensional space for a neutron in electromagnetic fields. Mod Phys Lett A, 1990, 5: 2361鈥?370 CrossRef
  36. Watson G N. Theory of Bessel Function. London: Cambrige University Press, 1952
  37. Wliczek F. Magnetic flux, angular momentum, and statistics. Phys Rev Lett, 1982, 48: 1144鈥?146; Wliczek F. Quantum mechanics of fractional-spin particles. Phys Rev Lett, 1982, 49: 957鈥?59 CrossRef
  
• 作者单位：JunLi Xin (1) (2)
  JiuQing Liang (1)
  
  1. Institute of Theoretical Physics, Shanxi University, Taiyuan, 030006, China
  2. Department of Physics and Electronic Engineering, Yuncheng University, Yuncheng, 044000, China
  
• ISSN：1869-1927

文摘

In this paper we present both the classical and quantum periodic-orbits of a neutral spinning particle constrained in two-dimensional central-potentials with a cylindrically symmetric electric-field in addition, which leads to an effective non-Abelian gauge field generated by the spin-orbit coupling. Coherent superposition of orbital angular-eigenfunctions obtained explicitly under the condition of zero-energy exhibits the quantum-classical correspondence in the meaning of exact coincidence between classical orbits and spatial patterns of quantum wave-functions, which as a consequence results in the fractional quantization of orbital angular-momentum by the requirement of the same rotational symmetry of quantum and classical orbits. A non-Abelian anyon-model emerges in a natural way.