Critical Dimensionality for Normal Fluctuations of Macrovariables in Nonequilibrium States

概要

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The scaling condition for the normal fluctuations of macrovariables is studied by regarding the spatial dimensionality d for fluctuations as a variable parameter. The critical dimensionality d_c, above which the fluctuations are normal and obey a Gaussian process and below which they are anomalous and obey a nonlinear non-Gaussian process, is defined and explored for nonequilibrium inhomogeneous systems with the aid of a scaling theory of the dependence of macrovariables on their spatial cutoff. It is shown that d_c=Max_μ[2α_μ+γ_μ], where α_μ and γ_μ are the scaling exponents of the deterministic part and those of the pair correlation functions for d≧d_c, respectively. It turns out that d_c=1 in the kinetic region of the particle density in μ space of low-density gases with short-range forces, d_c=2 in the non-critical region of laminar hydrodynamic flows, and d_c=4 in the critical region of the Benard-Rayleigh instability and of the Schlogl chemical instability. It is shown that there are two types of critical fluctuations, both of which have an identical value of d_c, but which have quite different features from each other.
理論物理学刊行会の論文
1977-03-25