Mean-field approximation for spacing distribution functions in classical systems
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.
- Publication:
-
Physical Review E
- Pub Date:
- January 2012
- DOI:
- 10.1103/PhysRevE.85.011151
- arXiv:
- arXiv:1111.5212
- Bibcode:
- 2012PhRvE..85a1151G
- Keywords:
-
- 05.40.-a;
- 68.55.A-;
- 68.35.-p;
- 81.15.Aa;
- Fluctuation phenomena random processes noise and Brownian motion;
- Nucleation and growth;
- Solid surfaces and solid-solid interfaces: Structure and energetics;
- Theory and models of film growth;
- Condensed Matter - Statistical Mechanics
- E-Print:
- Phys. Rev. E 85, 011151 (2012)