Wigner crystallization in the quantum 1D jellium at all densities

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.

20 pages, 3 figures, to appear in Communications in Mathematical Physics

References in corpus (1)

• Symmetry breaking in quasi-1D Coulomb systems

Cited by in corpus (6)

• Coulomb and Riesz gases: The known and the unknown
• Macroscopic and edge behavior of a planar jellium
• At the edge of a one-dimensional jellium
• Periodic energy minimizers for a one-dimensional liquid drop model
• Interface dynamics of a metastable mass-conserving spatially extended diffusion
• Large deviations in the quantum quasi-1D jellium