Statistical Properties of Trajectories of Friendly Walkers on Spatio-Temporal Plane : General Physics
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概要
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Friendly walkers are the non-crossing random walkers on a lattice with attractive interactions. We characterize each trajectory of friendly walkers by the number of walkers m, the time interval of observation t and the total length of trajectory r. A new algorithm to generate trajectories on a spatio-temporal plane is proposed and the distribution function of number of distinct trajectories characterized by (m, t, r), f_<m,t>(r), is estimated by a random sampling method. The variance, the skewness and the kurtosis of f_<m,t>(r) converge to finite values without scaling as t ⇾ ∞ for each m. The distribution is asymmetric and its tails are expressed by stretched exponential functions. We consider the canonical distribution of m friendly walkers by introducing a parameter p which plays the same role of the Boltzmann factor e^<-β> in the usual equilibrium systems. We calculate the mean and variance of r in the canonical distribution as a function of p for each m at t. It is observed that the variance of r per unit time interval has a peak at a certain value of p for each m = 2, 3, 4 and 5. We discuss the possibility that the peak indicates the phase transition of trajectories of friendly walkers realized on a spatio-temporal plane.
- 社団法人日本物理学会の論文
- 2001-01-15
著者
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Katori Makoto
Department Of Pharmacology Kitasato University School Of Medicine
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INUl Norio
Department of Mechanical and Intelligent Engineering,Himeji Institute of Technology
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