Alternative routes to equivalent classical models of a quantum system

doi:10.1088/1674-1056/21/12/120301

Chin. Phys. B ›› 2012, Vol. 21 ›› Issue (12): 120301-120301.doi: 10.1088/1674-1056/21/12/120301

Alternative routes to equivalent classical models of a quantum system

M. Radonjić, Slobodan Prvanović, Nikola Burić

a Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
b Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China

收稿日期:2012-05-30 修回日期:2012-07-03 出版日期:2012-11-01 发布日期:2012-11-01
基金资助:
Project supported by the Ministry of Education and Science of the Republic of Serbia (Grant Nos. 171017, 171028, 171038, and III45016). We would like to acknowledge partial support by COST (Action MP1006).

Alternative routes to equivalent classical models of a quantum system

M. Radonjić, Slobodan Prvanović, Nikola Burić

a Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
b Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China

Received:2012-05-30 Revised:2012-07-03 Online:2012-11-01 Published:2012-11-01
Contact: Nikola Burić E-mail:buric@ipb.ac.rs
Supported by:
Project supported by the Ministry of Education and Science of the Republic of Serbia (Grant Nos. 171017, 171028, 171038, and III45016). We would like to acknowledge partial support by COST (Action MP1006).

摘要/Abstract

摘要： Coarse-graining of some sort is the fundamental and unavoidable step in any attempt to derive the classical mechanical behavior from the quantum formalism. We utilize two-mode Bose-Hubbard model to illustrate how different coarse-grained systems can be naturally associated with a fixed quantum system if it is compatible with different dynamical algebras. Alternative coarse-grained systems generate different evolutions of the same physical quantities, and the difference becomes negligible only in the appropriate macro-limit.

关键词: two-mode Bose-Hubbard model, coarse-grained system, Hamilton operator, system dynamical algebra

Abstract: Coarse-graining of some sort is the fundamental and unavoidable step in any attempt to derive the classical mechanical behavior from the quantum formalism. We utilize two-mode Bose-Hubbard model to illustrate how different coarse-grained systems can be naturally associated with a fixed quantum system if it is compatible with different dynamical algebras. Alternative coarse-grained systems generate different evolutions of the same physical quantities, and the difference becomes negligible only in the appropriate macro-limit.

Key words: two-mode Bose-Hubbard model, coarse-grained system, Hamilton operator, system dynamical algebra

中图分类号: (Algebraic methods)

03.65.Fd

03.65.Sq (Semiclassical theories and applications)

M. Radonjić, Slobodan Prvanović, Nikola Burić. Alternative routes to equivalent classical models of a quantum system[J]. Chin. Phys. B, 2012, 21(12): 120301-120301.

参考文献 20

[1]	Landsman N P 1998 Mathematical Topics Between Classical and Quantum Mechanics (New York: Springer-Verlag)
[2]	Zurek W H 2003 Rev. Mod. Phys. 73 715
[3]	Schlosshauer M 2007 Decoherence and the Quantum-to-Classical Transition (Berlin: Springer)
[4]	Bassi A and Ghirardi G 2003 Phys. Rep. 379 257
[5]	Percival I C 1999 Quantum State Difussion (Cambridge: Cambridge University Press)
[6]	Kofler J and Brukner Č 2008 Phys. Rev. Lett. 101 090403.
[7]	Hornberger K, Gerlich S, Haslinger P, Nimmrichter S and Arndt M 2012 Rev. Mod. Phys. 84 157
[8]	O'Connell A D, Hofheinz M, Ansmann M, Radoslaw C, Bialczak C, Lenander M, Lucero E, Neeley M, Sank D, Wang H, Weides M, Wenner J, Martinis J M and Cleland A N 2010 Nature 464 697
[9]	Poot M and van der Zant H S J 2012 Phys. Rep. 511 273
[10]	Radonjić M, Prvanović S and Burić N 2011 Phys. Rev. A 84 022103
[11]	Radonjić M, Prvanović S and Burić N 2012 Phys. Rev. A 85 022117
[12]	Burić N 2011 Chin. Phys. B 20 120306
[13]	Albiez M, Gati R, Fölling J, Hunsmann S, Cristiani M and Oberthaler M K 2005 Phys. Rev. Lett. 95 010402
[14]	Gati R, Hemmerling B, Fölling J, Albiez M and Oberthaler M K 2006 Phys. Rev. Lett. 96 130404
[15]	Burić N 2008 Ann. Phys. (NY) 233 17
[16]	Brody D C, Gustavsson A C T and Hughston L 2008 J. Phys. A 41 475301
[17]	Brody D C and Hughston L P 2001 J. Geom. Phys. 38 19
[18]	Liu J, Wu B and Niu Q 2003 Phys. Rev. Lett. 90 170404
[19]	Wu B, Liu J and Niu Q 2005 Phys. Rev. Lett. 94 140402
[20]	Perelomov A M 1986 Generalized Coherent States and Their Applications (Berlin: Springer-Verlag)

Alternative routes to equivalent classical models of a quantum system

Alternative routes to equivalent classical models of a quantum system

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 20

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Luhong Su(苏鹭红), Cui-Xian Guo(郭翠仙), Yongliang Wang(王永良), Li Li(李力), Xinhui Ruan(阮馨慧), Yanjing Du(杜燕京), Shu Chen(陈澍), and Dongning Zheng(郑东宁). Observation of size-dependent boundary effects in non-Hermitian electric circuits[J]. 中国物理B, 2023, 32(3): 38401-038401.
[2]	Jie-Hui Huang(黄接辉), Li-Guo Qin(秦立国), Guang-Long Chen(陈光龙), Li-Yun Hu(胡利云), and Fu-Yao Liu(刘福窑). Quantum speed limit for mixed states in a unitary system[J]. 中国物理B, 2022, 31(11): 110307-110307.
[3]	Cui-Xian Guo(郭翠仙) and Shu Chen(陈澍). Exact solutions of non-Hermitian chains with asymmetric long-range hopping under specific boundary conditions[J]. 中国物理B, 2022, 31(1): 10313-010313.
[4]	Bing-Sheng Lin(林冰生) and Tai-Hua Heng(衡太骅). Connes distance of 2D harmonic oscillators in quantum phase space[J]. 中国物理B, 2021, 30(11): 110203-110203.
[5]	Jing-Ying Wei(魏静莹), Qing Wang(王青), and Jian Jing(荆坚). Supersymmetric structures of Dirac oscillators in commutative and noncommutative spaces[J]. 中国物理B, 2021, 30(11): 110307-110307.
[6]	Jafari Matehkolaee Mehdi. Introducing the general condition for an operator in curved space to be unitary[J]. 中国物理B, 2021, 30(8): 80301-080301.
[7]	Noah F. Q. Yuan. Projective representation of D₆ group in twisted bilayer graphene[J]. 中国物理B, 2021, 30(7): 70311-070311.
[8]	Jian-Jian Cheng(程剑剑), Yao Du(杜瑶), and Lin Zhang(张林). Lie transformation on shortcut to adiabaticity in parametric driving quantum systems[J]. 中国物理B, 2021, 30(6): 60302-060302.
[9]	Fa-Kai Wen(温发楷) and Xin Zhang(张鑫). Exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions[J]. 中国物理B, 2021, 30(5): 50201-050201.
[10]	M Eshghi,R Sever,S M Ikhdair. Energy states of the Hulthen plus Coulomb-like potential with position-dependent mass function in external magnetic fields[J]. 中国物理B, 2018, 27(2): 20301-020301.
[11]	M Baradaran,H Panahi. Solvability of a class of PT-symmetric non-Hermitian Hamiltonians: Bethe ansatz method[J]. 中国物理B, 2017, 26(6): 60301-060301.
[12]	郭光杰, 孟艳, 常虹, 段会增, 邸冰. Inverse problem of quadratic time-dependent Hamiltonians[J]. 中国物理B, 2015, 24(8): 80301-080301.
[13]	H. Panahi, S. Zarrinkamar, M. Baradaran. Solutions of the D-dimensional Schrödinger equation with Killingbeck potential: Lie algebraic approach[J]. 中国物理B, 2015, 24(6): 60301-060301.
[14]	杨彦敏, 马海涛, 林冰生, 郑驻军. Cluster algebra structure on the finite dimensional representations of affine quantum group U_q(Â₃)[J]. , 2015, 24(1): 10201-010201.
[15]	L. B. Castro, A. S. de Castro. Unsuitable use of spin and pseudospin symmetries with a pseudoscalar Cornell potential[J]. , 2014, 23(9): 90301-090301.