NDLI: Exact solutions for driven-diffusive systems: Excess-mass formation and phase transitions

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Exact solutions for driven-diffusive systems: Excess-mass formation and phase transitions

Content Provider	Semantic Scholar
Author	Woelki, Marko
Copyright Year	2009
Abstract	Zugriff auf den Volltext ist aus datenschutzrechtlichen Grunden gesperrt, neue Version unter DuEPublico-ID 31005 A totally asymmetric exclusion process on a ring is investigated in which particles can move one or two sites. Special attention is spent to the high-speed case where particles are not allowed to move a single site if they could move two sites. The stationary state is calculated exactly in the framework of the matrix-product ansatz. Independently of the update this process evolves into subspace of the configuration space and can lead to the formation of an excess hole. One observes two phases where its velocity takes different values which are calculated exactly from the normalization-generating function. Numerically computed density profiles show an interesting algebraic form as a limit of a shock profile. For continuous time the process turns out to be related to the ASEP with a single defect particle and for synchronous update it leads to a natural defect dynamics. For the general definition of the process with maximum velocity two, from an exact analysis of the two-particle sector we find that the distribution of inter-particle distance can oscillate. This is underlined in the thermodynamic limit by an improved mean-field theory which shows a remarkably good agreement with simulations. The main focus of this work is the exact solution of lattice models by matrix-product ansatz. We finally obtain stationary states also for related processes. Especially considerable is a new formulation of steady states for parallel dynamics like the ASEP with open boundaries as a product of a pair-factorized and a matrix-product state.
File Format	PDF HTM / HTML
Alternate Webpage(s)	https://duepublico.uni-duisburg-essen.de/servlets/DerivateServlet/Derivate-32933/diss_woelki.pdf
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article

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