Nonequilibrium Phase Transitions and Chemical Reactions

概要

論文の詳細を見る
The principal bifurcations occurring in reaction-diffusion systems away from equilibrium are reviewed. The effect of fluctuations on the bifurcation is investigated using a master equation approach. The following situations are envisaged: (i) All-or-none transitions in bistable spatially homogeneous systems. The behavior of the variance below and at the bifurcation point is discussed. The condition of coexistence of simultaneously stable states is shown to yield a relation between parameters which differs from the Maxwell type construction inferred from the deterministic equations. It is pointed out that in the thermodynamic limit the master equation displays two distinct solutions. (ii) Hopf bifurcations leading to limit cycles in spatially homogeneous systems. Numerical results are reported illustrating the structure of the "probability crater" descriptive of the limit cycle. It is suggested that in the thermodynamic limit, in addition to the static solution given by the probability crater there is a one-parameter family of time-dependent solutions rotating along the limit cycle. (iii) Spatially distributed systems. The effect of diffusion on all-or-none transitions is discussed using an extension of mean-field theory in conjunction with Monte-Carlo simulations.
理論物理学刊行会の論文
1979-04-01