Spontaneous Breaking of Translational Invariance and Spatial Condensation in Stationary States on a Ring: I. The Neutral System

TL;DR

This paper investigates a model of charged particles on a ring, revealing three distinct phases including a translational symmetry-breaking condensate, with analysis supported by algebraic, mean-field, and simulation methods.

Contribution

It introduces a detailed analysis of phase behavior in a charged particle model, highlighting spontaneous symmetry breaking and phase transitions akin to Bose-Einstein condensation.

Findings

Identification of three phases: pure, mixed, and disordered.

Discovery of a second-order phase transition with Bose-Einstein-like properties.

Observation of translational invariance breaking and spatial condensation.

Abstract

We consider a model in which positive and negative particles with equal densities diffuse in an asymmetric, CP invariant way on a ring. The positive particles hop clockwise, the negative counter-clockwise and oppositely-charged adjacent particles may swap positions. The model depends on two parameters. Analytic calculations using quadratic algebras, inhomogeneous solutions of the mean-field equations and Monte-Carlo simulations suggest that the model has three phases. A pure phase in which one has three pinned blocks of only positive, negative particles and vacancies and in which translational invariance is broken. A mixed phase in which the current has a linear dependence on one parameter but is independent of the other one and of the density of the charged particles. In this phase one has a bump and a fluid. The bump (condensate) contains positive and negative particles only, the fluid contains charged particles and vacancies uniformly distributed. The mixed phase is separated from the disordered phase by a second-order phase-transition which has many properties of the Bose-Einstein phase-transition observed in equilibrium. Various critical exponents are found.