Phase transition in annihilation-limited
processes |
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Authors: | M Khorrami A Aghamohammadi |
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Institution: | (1) Department of Physics, Alzahra University, Tehran, 1993891167, Iran |
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Abstract: | A system of particles is studied in which the stochastic
processes are one-particle type-change (or one-particle diffusion)
and multi-particle annihilation. It is shown that, if the
annihilation rate tends to zero but the initial values of the
average number of the particles tend to infinity, so that the
annihilation rate times a certain power of the initial values of
the average number of the particles remain constant (the double
scaling) then if the initial state of the system is a
multi-Poisson distribution, the system always remains in a state
of multi-Poisson distribution, but with evolving parameters. The
large time behavior of the system is also investigated. The system
exhibits a dynamical phase transition. It is seen that for a
k-particle annihilation, if k is larger than a critical value
kc, which is determined by the type-change rates,
then annihilation does not enter the relaxation exponent of the
system; while for k < kc, it is the annihilation (in
fact k itself) which determines the relaxation exponent. |
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Keywords: | 05 40 -a Fluctuation phenomena random processes noise and Brownian motion 02 50 Ga Markov processes |
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