Broken ergodicity in driven one-dimensional particle systems with short-range interaction

Rákos, Attila Gábor and Schütz, G. M. (2006) Broken ergodicity in driven one-dimensional particle systems with short-range interaction. Markov Processes and Related Fields, 12. pp. 309-322. ISSN 1024-2953

Preview

Text 1117069.pdf Download (248kB) | Preview

Abstract

We present a one-dimensional nonequilibrium model for a driven di�usive system which has local interactions and slow nonconservative reaction kinetics. Monte-Carlo simulations suggest that in the thermodynamic limit the steady state exhibits a phase with broken ergodicity. We propose a hydrodynamic equation for the coarse-grained density (under Eulerian scaling), augmented by a prescription how to treat shock and boundary discontinuities, respectively. This conjecture can be readily generalized to other weakly nonconservative driven di�usive systems and is supported by a heuristic identi�cation of the main dynamical mode that governs the microscopic dynamics, viz. the random motion of a shock in an self-organized e�ective potential. This picture leads to the exact phase diagram of the system and suggests a novel and mathematically tractable mechanism for \freezing by heating".

Actions (login required)

Edit Item