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Abstract
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 drivendiffusive systemswhich includes exclusion processesfocusing 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 matrixproduct form. In addition to a gentle introduction to this matrixproduct 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 freeenergy functionals, the classification of exclusion processes involving multiple particle species, existence proofs of a matrixproduct state for a given model and more complicated variants of the matrixproduct state that allow various types of parallel dynamics to be handled. We conclude with a brief discussion of open problems for future research.
Original language  English 

Pages (fromto)  R333R441 
Number of pages  109 
Journal  Journal of physics aMathematical and theoretical 
Volume  40 
Issue number  46 
DOIs  
Publication status  Published  16 Nov 2007 
Keywords
 ASYMMETRIC SIMPLEEXCLUSION
 DRIVEN DIFFUSIVE SYSTEMS
 SPONTANEOUS SYMMETRYBREAKING
 FINITEDIMENSIONAL REPRESENTATIONS
 BETHEANSATZ SOLUTION
 QUANTUM SPIN CHAINS
 ZERORANGE PROCESS
 YANGLEE THEORY
 OPEN BOUNDARIES
 PHASETRANSITIONS
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Dive into the research topics of 'Nonequilibrium steady states of matrixproduct form: a solver's guide'. Together they form a unique fingerprint.Projects
 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
Project: Research