  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.
