Nonuniform autonomous one-dimensional exclusion nearest-neighbor reaction-diffusion models
Abstract
The most general nonuniform reaction-diffusion models on a one-dimensional lattice with boundaries, for which the time evolution equations of correlation functions are closed, are considered. A transfer matrix method is used to find the static solution. It is seen that this transfer matrix can be obtained in a closed form, if the reaction rates satisfy certain conditions. We call such models superautonomous. Possible static phase transitions of such models are investigated. At the end, as an example of superautonomous models, a nonuniform voter model is introduced, and solved explicitly.
- Publication:
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European Physical Journal B
- Pub Date:
- March 2010
- DOI:
- 10.1140/epjb/e2010-00061-2
- arXiv:
- arXiv:1002.0059
- Bibcode:
- 2010EPJB...74..159A
- Keywords:
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- Condensed Matter - Statistical Mechanics
- E-Print:
- 14 pages