474 citations · 1.9k across the 45 of their papers we have counts for
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Spontaneous Breaking of Translational Invariance and Spatial Condensation in Stationary States on a Ring: I. The Neutral System
Peter F. Arndt, Thomas Heinzel, Vladimir Rittenberg
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 ne…
Metastability and spinodal points for a random walker on a triangle
Peter F. Arndt, Thomas Heinzel
We investigate time-dependent properties of a single particle model in which a random walker moves on a triangle and is subjected to non-local boundary conditions. This model exhib…
Spontaneous Breaking of Translational Invariance in One-Dimensional Stationary States on a Ring
Peter F. Arndt, Thomas Heinzel, Vladimir Rittenberg
We consider a model in which positive and negative particles diffuse in an asymmetric, CP-invariant way on a ring. The positive particles hop clockwise, the negative counterclockwi…
First-order phase transitions in one-dimensional steady states
Peter F. Arndt, Thomas Heinzel, Vladimir Rittenberg
The steady states of the two-species (positive and negative particles) asymmetric exclusion model of Evans, Foster, Godreche and Mukamel are studied using Monte Carlo simulations.…
Stochastic Models on a Ring and Quadratic Algebras. The Three Species Diffusion Problem
Peter F. Arndt, Thomas Heinzel, Vladimir Rittenberg
The stationary state of a stochastic process on a ring can be expressed using traces of monomials of an associative algebra defined by quadratic relations. If one considers only ex…