Entangled state representation for mesoscopic persistent  current  ring   and its phase-angular momentum

WU Weifeng; FAN Hongyi

doi:10.3969/j.issn.0253-2778.2016.08.005

JUSTC > 2016 > 46(8): 652-656. > DOI: 10.3969/j.issn.0253-2778.2016.08.005

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Entangled state representation for mesoscopic persistent current ring and its phase-angular momentum

1.
College of Mechanical and Electrical Engineering, Chizhou University, Chizhou 247000, China
2.
Department of Materials Science and Engineering, University of Science and Technology of China, Hefei 230026, China

Cite this: JUSTC, 2016, 46(8): 652-656

https://doi.org/10.3969/j.issn.0253-2778.2016.08.005

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Received Date: January 28, 2016
Revised Date: May 20, 2016
Accepted Date: May 20, 2016
Published Date: August 29, 2016

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Abstract

Abstract

The entangled state representation was establish,in which the phase operator and the angular momentum operator have been applied, to realize the phase-angular momentum quantization of mesoscopic persistent current ring (MPCR) , and derive its energy spectrum. In addition,it was revealed that the ascending/lowering of angular momentum corresponds to the currents increase/decrease through angular momentum representation for the persistent current ring.

Abstract

The entangled state representation was establish,in which the phase operator and the angular momentum operator have been applied, to realize the phase-angular momentum quantization of mesoscopic persistent current ring (MPCR) , and derive its energy spectrum. In addition,it was revealed that the ascending/lowering of angular momentum corresponds to the currents increase/decrease through angular momentum representation for the persistent current ring.

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References (17)

References

[1]	AHARONOV Y, BOHM D. Significance of electromagnetic potentials in the quantum theory [J]. Phys Rev, 1959, 115: 485-491.
[2]	BTTIKER M, IMRY Y, LANDAUER R, et al. Generalized many-channel conductance formula with application to small rings [J]. Phys Rev B, 1985, 31: 6 207-6 215.
[3]	AHARONOV Y, CASHER A. Topological quantum effects for neutral particles [J] Phys Rev Lett, 1984, 53: 319-321.
[4]	REZNIK B, AHARINOV Y. Question of the nonlocality of the Aharonov-Casher effect[J]. Phys Rev D, 1989, 40: 4 178-4 183.
[5]	DEO P S, JAYANNAVAR A M. Quantum waveguide transport in serial stub and loop structures[J]. Phys Rev B, 1994, 50:11629.
[6]	DEO P S, JAYANNAVAR A M. Persistent currents in the presence of a transport current[J]. Phys Rev B, 1995, 51:10175.
[7]	TAKAI D, OHTA K. Quantum transport through a one-dimensional ring with tunnel junctions[J]. Phys Rev B, 1995, 51:11132.
[8]	MA Mingming, DING Jianwen, CHEN Hongbo, et al. Effects of gradient disorder on persistent currents in two-dimensional mesoscopic rings[J]. Acta Phys Sin, 2009, 58(4): 2 226-2 230. 马明明, 丁建文, 陈宏波,等. 二维介观环中持续电流的梯度无序效应[J]. 物理学报，2009, 58(4):2 226-2 230.
[9]	WU Shaoquan, HE Zhong, YAN Conghua, et al. Kondo effect in parallel double quantum dots embedded in a mesoscopic ring [J] Acta Phys Sin，2006，55(3): 1 413-1 418. 吴绍全,何忠,阎从华，等. 嵌入并联耦合双量子点介观环系统中的近藤效应[J].物理学报，2006，55(3):1 413-1 418.
[10]	FU Bang, DENG Wenji. General solutions to spin transportation of electrons through equilateral polygon quantum rings with Rashba spin-orbit interaction[J]. Acta Phys Sin, 2010, 59(4):2 739-2 745. 付邦,邓文基. 任意正多边形量子环自旋输运的普遍解[J].物理学报，2010, 59(4):2 739-2 745.
[11]	HUANG Rui, WU Shaoquan. Spin-polarized transport through T-shaped quantum dot system[J]. Chinese Journal of Low Temperature Physics, 2010,32（4）：284-288. 黄睿,吴绍全. Ｔ型量子点结构中的自旋极化输运过程[J]. 低温物理学报, 2010,32（4）：284-288.
[12]	DAI Nan, DENG Wenji. Persistent currents in mesoscopic graphene rings with armchair edges[J]. Acta Phys Sin, 2015, 64(1): 017302. 代楠,邓文基.扶手椅型石墨烯介观环中的持续电流[J].物理学报，2015, 64(1): 017302.
[13]	JOHNSON M H, LIPPMANN B A. Motion in a constant magnetic field[J]. Physical Review, 1946, 76: 828-832.
[14]	LOUISELL W H. Quantum Statistical Properties of Radiation [M].New York: John Wiley, 1973
[15]	FAN H Y, KLAUDER J R.Eigenvectors of two particless relative position and total momentum[J]. Phys Rev A,1994, 49: 704-707.
[16]	FAN Hongyi, FAN Yue.Representation of two-mode squeezing operator[J]. Phys Rev A, 1996, 54: 958-960.
[17]	FAN Hongyi. Phase state as a cooper-pair number: Phase minimum uncertainty state for Josephson junction[J]. Inter J Mod Phys B, 2003, 17: 2 599-2 608.)

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References

[1]	AHARONOV Y, BOHM D. Significance of electromagnetic potentials in the quantum theory [J]. Phys Rev, 1959, 115: 485-491.
[2]	BTTIKER M, IMRY Y, LANDAUER R, et al. Generalized many-channel conductance formula with application to small rings [J]. Phys Rev B, 1985, 31: 6 207-6 215.
[3]	AHARONOV Y, CASHER A. Topological quantum effects for neutral particles [J] Phys Rev Lett, 1984, 53: 319-321.
[4]	REZNIK B, AHARINOV Y. Question of the nonlocality of the Aharonov-Casher effect[J]. Phys Rev D, 1989, 40: 4 178-4 183.
[5]	DEO P S, JAYANNAVAR A M. Quantum waveguide transport in serial stub and loop structures[J]. Phys Rev B, 1994, 50:11629.
[6]	DEO P S, JAYANNAVAR A M. Persistent currents in the presence of a transport current[J]. Phys Rev B, 1995, 51:10175.
[7]	TAKAI D, OHTA K. Quantum transport through a one-dimensional ring with tunnel junctions[J]. Phys Rev B, 1995, 51:11132.
[8]	MA Mingming, DING Jianwen, CHEN Hongbo, et al. Effects of gradient disorder on persistent currents in two-dimensional mesoscopic rings[J]. Acta Phys Sin, 2009, 58(4): 2 226-2 230. 马明明, 丁建文, 陈宏波,等. 二维介观环中持续电流的梯度无序效应[J]. 物理学报，2009, 58(4):2 226-2 230.
[9]	WU Shaoquan, HE Zhong, YAN Conghua, et al. Kondo effect in parallel double quantum dots embedded in a mesoscopic ring [J] Acta Phys Sin，2006，55(3): 1 413-1 418. 吴绍全,何忠,阎从华，等. 嵌入并联耦合双量子点介观环系统中的近藤效应[J].物理学报，2006，55(3):1 413-1 418.
[10]	FU Bang, DENG Wenji. General solutions to spin transportation of electrons through equilateral polygon quantum rings with Rashba spin-orbit interaction[J]. Acta Phys Sin, 2010, 59(4):2 739-2 745. 付邦,邓文基. 任意正多边形量子环自旋输运的普遍解[J].物理学报，2010, 59(4):2 739-2 745.
[11]	HUANG Rui, WU Shaoquan. Spin-polarized transport through T-shaped quantum dot system[J]. Chinese Journal of Low Temperature Physics, 2010,32（4）：284-288. 黄睿,吴绍全. Ｔ型量子点结构中的自旋极化输运过程[J]. 低温物理学报, 2010,32（4）：284-288.
[12]	DAI Nan, DENG Wenji. Persistent currents in mesoscopic graphene rings with armchair edges[J]. Acta Phys Sin, 2015, 64(1): 017302. 代楠,邓文基.扶手椅型石墨烯介观环中的持续电流[J].物理学报，2015, 64(1): 017302.
[13]	JOHNSON M H, LIPPMANN B A. Motion in a constant magnetic field[J]. Physical Review, 1946, 76: 828-832.
[14]	LOUISELL W H. Quantum Statistical Properties of Radiation [M].New York: John Wiley, 1973
[15]	FAN H Y, KLAUDER J R.Eigenvectors of two particless relative position and total momentum[J]. Phys Rev A,1994, 49: 704-707.
[16]	FAN Hongyi, FAN Yue.Representation of two-mode squeezing operator[J]. Phys Rev A, 1996, 54: 958-960.
[17]	FAN Hongyi. Phase state as a cooper-pair number: Phase minimum uncertainty state for Josephson junction[J]. Inter J Mod Phys B, 2003, 17: 2 599-2 608.)

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