由微观随机动力学导出非平衡稳定态的长程相关性(Ⅰ) 用随机点阵气模型构造出宏观涨落流体力学理论

LONG RANGE CORRELATIONS FOR MICROSCOPIC STOCHA-STIC DYNAMICS IN A NONEQUILIBRIUM STEADY STATE (Ⅰ) CONSTRUCTION OF THE THEORY OF FLUCTUATING HYDRODYNAMICS IN TERMS OF A STOCHASTIC LATTICE GAS MODEL

研究了在一个平板上具有单独局域守恒场(即随机点阵气模型)的系统。在该平板的两个表面上保持着不同的密度,依据涨落流体力学理论,本文证明了其静态密度-密度相关是长程的。且当其维数d≥3时,该静态密度-密度相关是按-1//x-y/^(d-1)衰减。研究了随机点阵气模型在非平衡稳定态中的长程相关性,并构造出纯粹宏观的涨落流体力学理论。

We consider a system with a single locally conservative field in a slab geometry with different densities maintained at the two surfaces of the slab. On the basis of flutuating hydro-dynamics, we show that the static-density correlations are long ranged and decay as - l/│x-y│^(d-2) for dimension d≥3 over distances small compared to the size of the slab.