Projects per year
We consider the general problem of determining the steady state of stochastic nonequilibrium systems such as those that have been used to model ( among other things) biological transport and traffic flow. We begin with a broad overview of this class of driven-diffusive systems-which includes exclusion processes-focusing on interesting physical properties, such as shocks and phase transitions. We then turn our attention specifically to those models for which the exact distribution of microstates in the steady state can be expressed in a matrix-product form. In addition to a gentle introduction to this matrix-product approach, how it works and how it relates to similar constructions that arise in other physical contexts, we present a unified, pedagogical account of the various means by which the statistical mechanical calculations of macroscopic physical quantities are actually performed. We also review a number of more advanced topics, including nonequilibrium free-energy functionals, the classification of exclusion processes involving multiple particle species, existence proofs of a matrix-product state for a given model and more complicated variants of the matrix-product state that allow various types of parallel dynamics to be handled. We conclude with a brief discussion of open problems for future research.
|Number of pages||109|
|Journal||Journal of physics a-Mathematical and theoretical|
|Publication status||Published - 16 Nov 2007|
- ASYMMETRIC SIMPLE-EXCLUSION
- DRIVEN DIFFUSIVE SYSTEMS
- SPONTANEOUS SYMMETRY-BREAKING
- FINITE-DIMENSIONAL REPRESENTATIONS
- BETHE-ANSATZ SOLUTION
- QUANTUM SPIN CHAINS
- ZERO-RANGE PROCESS
- YANG-LEE THEORY
- OPEN BOUNDARIES
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- 1 Finished
Edinburgh Soft Matter and Statistical Physics Group: Programme Grant
Cates, M., Ackland, G., Egelhaaf, S., Evans, M., Poon, W. & Pusey, P.
1/10/03 → 31/03/08