Time-dependent perturbation theory for nonequilibrium lattice models |
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Authors: | Iwan Jensen Ronald Dickman |
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Institution: | (1) Department of Physics and Astronomy, Herbert H. Lehman College, City University of New York, 10468 Bronx, New York;(2) Institute of Physics, University of Aarhus, DK-8000 Aarhus C, Denmark |
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Abstract: | We develop a time-dependent perturbation theory for nonequilibrium interacting particle systems. We focus on models such as the contact process which evolve via destruction and autocatalytic creation of particles. At a critical value of the destruction rate there is a continuous phase transition between an active steady state and the vacuum state, which is absorbing. We present several methods for deriving series for the evolution starting from a single seed particle, including expansions for the ultimate survival probability in the super- and subcritical regions, expansions for the average number of particles in the subcritical region, and short-time expansions. Algorithms for computer generation of the various expansions are presented. Rather long series (24 terms or more) and precise estimates of critical parameters are presented. |
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Keywords: | Interacting particle systems nonequilibrium critical points series expansions Padé analysis |
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