Wigner crystallization in the quantum 1D jellium at all densities
Mathematical Physics
2014-09-17 v2 Statistical Mechanics
math.MP
Probability
Abstract
The jellium is a model, introduced by Wigner (1934), for a gas of electrons moving in a uniform neutralizing background of positive charge. Wigner suggested that the repulsion between electrons might lead to a broken translational symmetry. For classical one-dimensional systems this fact was proven by Kunz (1974), while in the quantum setting, Brascamp and Lieb (1975) proved translation symmetry breaking at low densities. Here, we prove translation symmetry breaking for the quantum one-dimensional jellium at all densities.
Cite
@article{arxiv.1306.6906,
title = {Wigner crystallization in the quantum 1D jellium at all densities},
author = {Sabine Jansen and Paul Jung},
journal= {arXiv preprint arXiv:1306.6906},
year = {2014}
}
Comments
20 pages, 3 figures, to appear in Communications in Mathematical Physics