Phase transitions in the one-dimensional coulomb gas ensembles
(2018) In Annals of Applied Probability 28(2). p.1249-1291- Abstract
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... (More)
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.
(Less)
- author
- Turova, Tatyana S. LU
- organization
- publishing date
- 2018-04-01
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Coulomb gas, Gibbs ensemble., Phase transitions
- in
- Annals of Applied Probability
- volume
- 28
- issue
- 2
- pages
- 43 pages
- publisher
- Institute of Mathematical Statistics
- external identifiers
-
- scopus:85046253733
- ISSN
- 1050-5164
- DOI
- 10.1214/17-AAP1329
- language
- English
- LU publication?
- yes
- id
- c33abb97-df0f-4639-8bd6-cedd5a4e4bda
- date added to LUP
- 2018-05-17 15:20:27
- date last changed
- 2022-01-31 03:28:43
@article{c33abb97-df0f-4639-8bd6-cedd5a4e4bda,
abstract = {{<p>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.</p>}},
author = {{Turova, Tatyana S.}},
issn = {{1050-5164}},
keywords = {{Coulomb gas; Gibbs ensemble.; Phase transitions}},
language = {{eng}},
month = {{04}},
number = {{2}},
pages = {{1249--1291}},
publisher = {{Institute of Mathematical Statistics}},
series = {{Annals of Applied Probability}},
title = {{Phase transitions in the one-dimensional coulomb gas ensembles}},
url = {{http://dx.doi.org/10.1214/17-AAP1329}},
doi = {{10.1214/17-AAP1329}},
volume = {{28}},
year = {{2018}},
}