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

• GENERAL • 上一篇    下一篇

Alternative routes to equivalent classical models of a quantum system

M. Radonjić, Slobodan Prvanović, Nikola Burić   

  1. 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   

  1. 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: 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)