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J. Phys. A: Math. Gen. 31 (1998) L45L51. Printed in the UK PII: S0305-4470(98)87053-4 LETTER TO THE EDITOR

Summary: J. Phys. A: Math. Gen. 31 (1998) L45­L51. Printed in the UK PII: S0305-4470(98)87053-4
Spontaneous breaking of translational invariance in
one-dimensional stationary states on a ring
Peter F Arndt§, Thomas Heinzel and Vladimir Rittenberg¶
Physikalisches Institut, Nußallee 12, 53115 Bonn, Germany
SISSA, Via Beirut 2­4, 34014 Trieste, Italy
Received 22 May 1997
Abstract. 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
counter-clockwise and oppositely-charged adjacent particles may swap positions. Monte Carlo
simulations and analytic calculations 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 spontaneously broken, a `mixed' phase with a non-vanishing
current in which the three blocks are positive, negative and neutral, and a disordered phase
without blocks.
Even if obtained from a master equation with local dynamics, stationary states are not
necessarily given by Gibbs ensembles. In cases where one has detailed balance, the
Hamiltonian may have long-range interactions. For these reasons, stationary states can
exhibit phase transitions even in one dimension. Spontaneous CP -symmetry breaking


Source: Arndt, Peter - Max-Planck-Institut für molekulare Genetik


Collections: Physics; Biotechnology