Wigner crystallization in the quantum 1D jellium at all densities (Q406656)

The jellium (model) has been introduced by Wigner to study gas of electrons, and here the authors deal with one-dimensional quantum jellium which describes uniformly charged parallel sheets moving possibly in the transverse direction. The main result of the paper is to prove crystallization for the quantum one-dimensional jellium at all densities and to this end they use the Krein-Rutman theorem applied to a transfer operator.