Phase transitions in the one-dimensional Coulomb gas ensembles
| Autor: | Tatyana S. Turova |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
Phase transition 82B21 01 natural sciences Gibbs ensemble 60F05 0103 physical sciences Coulomb FOS: Mathematics Limit (mathematics) Statistical physics 0101 mathematics Mathematics Central limit theorem Canonical ensemble 010102 general mathematics Probability (math.PR) Coulomb gas Boltzmann distribution Charged particle phase transitions Flow (mathematics) 82B26 010307 mathematical physics Statistics Probability and Uncertainty Mathematics - Probability |
| Zdroj: | Ann. Appl. Probab. 28, no. 2 (2018), 1249-1291 |
| Popis: | We consider the system of particles on a finite interval with pairwise nearest neighbours interaction and external force. This model was introduced by Malyshev [Probl. Inf. Transm. 51 (2015) 31–36] to study the flow of charged particles on a rigorous mathematical level. It is a simplified version of a 3-dimensional classical Coulomb gas model. We study Gibbs distribution at finite positive temperature extending recent results on the zero temperature case (ground states). We derive the asymptotics for the mean and for the variances of the distances between the neighbouring charges. We prove that depending on the strength of the external force there are several phase transitions in the local structure of the configuration of the particles in the limit when the number of particles goes to infinity. We identify 5 different phases for any positive temperature. ¶ The proofs rely on a conditional central limit theorem for nonidentical random variables, which has an interest on its own. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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