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Chin. Phys. B, 2014, Vol. 23(4): 040305    DOI: 10.1088/1674-1056/23/4/040305
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Analysis of dynamical properties for the two-site Bose–Hubbard model with an algebraic method

Meng Xiang-Jiaa, Feng Hai-Ranb, Zheng Yu-Juna
a School of Physics, Shandong University, Jinan 250100, China;
b Department of Physics and Information Engineering, Jining University, Qufu 273155, China
Abstract  In this work, we propose an algebraic recursion method to study the dynamical evolution of the two-site Bose-Hubbard model. We analyze its properties from the viewpoints of single partite purity, energy, and trace distance, in which the model is considered as a typical bipartite system. The analytical expressions for the quantities are derived. We show that the purity can well reflect the transition between different regimes for the system. In addition, we demonstrate that the transition from the delocalization regime to the self-trapping regime with the ratio η increasing not only happens for an initially local state but also for any initial states. Furthermore, we confirm that the dynamics of the system presents a periodicity for η=0 and the period is tc=π/2J when the initial state is symmetric.
Keywords:  two-site Bose-Hubbard system      dynamical evolution      purity      energy      trace distance  
Received:  15 June 2013      Revised:  17 September 2013      Accepted manuscript online: 
PACS:  03.75.Kk (Dynamic properties of condensates; collective and hydrodynamic excitations, superfluid flow)  
  03.75.Lm (Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations)  
  32.80.Pj  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 91021009 and 21073110).
Corresponding Authors:  Zheng Yu-Jun     E-mail:  yzheng@sdu.edu.cn
About author:  03.75.Kk; 03.75.Lm; 32.80.Pj

Cite this article: 

Meng Xiang-Jia, Feng Hai-Ran, Zheng Yu-Jun Analysis of dynamical properties for the two-site Bose–Hubbard model with an algebraic method 2014 Chin. Phys. B 23 040305

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