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Mean-field approximation for spacing distribution functions in classical systems
Diego Luis González1, Alberto Pimpinelli, T L Einstein
1Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA. dgonzal2@umd.edu
Abstract:
We propose a mean-field method to calculate approximately the spacing distribution functions p((n))(s) in one-dimensional classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation and the extended Wigner surmise. In our mean-field approach, p((n))(s) is calculated from a set of Langevin equations, which are decoupled by using a mean-field approximation. We find that in spite of its simplicity, the mean-field approximation provides good results in several systems. We offer many examples illustrating that the three previously mentioned methods give a reasonable description of the statistical behavior of the system. The physical interpretation of each method is also discussed.
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