中国物理B ›› 2020, Vol. 29 ›› Issue (8): 88904-088904.doi: 10.1088/1674-1056/ab8a41

• SPECIAL TOPIC—Ultracold atom and its application in precision measurement • 上一篇    

Finite density scaling laws of condensation phase transition in zero-range processes on scale-free networks

Guifeng Su(苏桂锋), Xiaowen Li(李晓温), Xiaobing Zhang(张小兵), Yi Zhang(张一)   

  1. 1 Department of Physics, Shanghai Normal University, Shanghai 200234, China;
    2 School of Physics, Nankai University, Tianjin 300071, China
  • 收稿日期:2020-01-08 修回日期:2020-04-06 出版日期:2020-08-05 发布日期:2020-08-05
  • 通讯作者: Yi Zhang E-mail:yizhang@shnu.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 11505115).

Finite density scaling laws of condensation phase transition in zero-range processes on scale-free networks

Guifeng Su(苏桂锋)1, Xiaowen Li(李晓温)1, Xiaobing Zhang(张小兵)2, Yi Zhang(张一)1   

  1. 1 Department of Physics, Shanghai Normal University, Shanghai 200234, China;
    2 School of Physics, Nankai University, Tianjin 300071, China
  • Received:2020-01-08 Revised:2020-04-06 Online:2020-08-05 Published:2020-08-05
  • Contact: Yi Zhang E-mail:yizhang@shnu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 11505115).

摘要: The dynamics of zero-range processes on complex networks is expected to be influenced by the topological structure of underlying networks. A real space complete condensation phase transition in the stationary state may occur. We study the finite density effects of the condensation transition in both the stationary and dynamical zero-range processes on scale-free networks. By means of grand canonical ensemble method, we predict analytically the scaling laws of the average occupation number with respect to the finite density for the steady state. We further explore the relaxation dynamics of the condensation phase transition. By applying the hierarchical evolution and scaling ansatz, a scaling law for the relaxation dynamics is predicted. Monte Carlo simulations are performed and the predicted density scaling laws are nicely validated.

关键词: finite density scaling, zero-range processes (ZRP), scale-free networks

Abstract: The dynamics of zero-range processes on complex networks is expected to be influenced by the topological structure of underlying networks. A real space complete condensation phase transition in the stationary state may occur. We study the finite density effects of the condensation transition in both the stationary and dynamical zero-range processes on scale-free networks. By means of grand canonical ensemble method, we predict analytically the scaling laws of the average occupation number with respect to the finite density for the steady state. We further explore the relaxation dynamics of the condensation phase transition. By applying the hierarchical evolution and scaling ansatz, a scaling law for the relaxation dynamics is predicted. Monte Carlo simulations are performed and the predicted density scaling laws are nicely validated.

Key words: finite density scaling, zero-range processes (ZRP), scale-free networks

中图分类号:  (Networks and genealogical trees)

  • 89.75.Hc
05.20.-y (Classical statistical mechanics) 02.50.Ey (Stochastic processes)