Abstract
The behavior of the most probable values of the order parameter x and the amplitude p of conjugate force fluctuations is studied for a stochastic system with a noise amplitude depending on x as |x|a. It is shown that the phase half-plane x>0 for the canonical pair x, p is divided into isolated regions of large, intermediate, and small values of x. In the first region, the trajectories converge to values of x, p → ∞ as the time t → ∞, and the probability of their realization is negligibly small. In the intermediate region, the configuration point tends to the attraction center corresponding to a stationary ordered state. In the region
, the trajectories converge to the point x=p=0 for 0<a<1/2 and to x=0, p → ∞ for 1/2<a≤1. In the former case, the probability of realization of trajectories is finite, while, in the latter case, it is negligibly small, and an absorbing state can be formed.
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Translated from Fizika Tverdogo Tela, Vol. 42, No. 3, 2000, pp. 520–526.
Original Russian Text Copyright © 2000 by Olemsko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l}\), Kharchenko.
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Olemskoi, A.I., Kharchenko, D.O. Kinetics of phase transitions with singular multiplicative noise. Phys. Solid State 42, 532–538 (2000). https://doi.org/10.1134/1.1131244
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DOI: https://doi.org/10.1134/1.1131244