Phase transitions in one-dimensional nonequilibrium systems

By M. Evans. 2000

303 citations recorded by the source corpus.

The phenomenon of phase transitions in one-dimensional systems is discussed. Equilibrium systems are reviewed and some properties of an energy function which may allow phase transitions and phase ordering in one dimension are identified. We then give an overview of the one-dimensional phase transitions which have been studied in nonequilibrium systems. A particularly simple model, the zero-range process, for which the steady state is known exactly as a product measure, is discussed in some detail. Generalisations of the model, for which a product measure still holds, are also discussed. We analyse in detail a condensation phase transition in the model and show how conditions under which it may occur may be related to the existence of an effective long-range energy function. It is also shown that even when the conditions for condensation are not fulfilled one can still observe very sharp crossover behaviour and apparent condensation in a finite system. Although the zero-range process is not well known within the physics community, several nonequilibrium models have been proposed that are examples of a zero-range process, or closely related to it, and we review these applications here.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e5be972cde14f21b12035eaf8865a62f84fe4c63

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Non-equilibrium steady states: fluctuations and large deviations of the density and of the current (2007, background): “The existence of phase transitions [64, 66, 67, 68] in these driven lattice gases is one of the striking properties of non-equilibrium steady states, as it is well known that one dimensional systems at equilibrium with short range interactions cannot exhibit phase transitions.”
Universality classes in nonequilibrium lattice systems (2002, background): “There are also other nonequilibrium phase transitions, for example, in lattice gases with currents sEvans et al., 1995, 1998; Kolomeisky et al., 1998; Evans, 2000d or in traffic models sChowdhury et al., 2000d, but in these systems the critical universality classes have not yet been explored.”
Tunneling and Metastability of Continuous Time Markov Chains (2009, unknown): “This family, known as the condensed zero-range processes, have been introduced in the physics literature [8, 13, 9] to model the Bose-Einstein condensation phenomena.”
Condensation in the Zero Range Process: Stationary and Dynamical Properties (2003, methodology): “For the model introduced in [7], we will analyze the statistical properties of the background phase in detail.”