分形分枝 Koch 曲线上的偏置超扩散(英文)

BIASED ULTRADIFFUSION ON A FRACTAL BRANCHING KOCH CURVE *

通过一个精确的重整Ｄｅｃｉｍａｔｉｏｎ程序，引入和分析了一个具有偏置项｛ηｉ｝分级集的分形分枝Ｋｏｃｈ曲线的超扩散模型．对于动力学输运，在固定点η０＝０处我们发现了两个新的渡越点．在另外一个固定点η０＝Ｗ０，自关联函数将由幂率关系衰变成指数关系，这里Ｗ０是分布于层次分形曲线上的第一级能级势垒｛Ｗｉ｝．

This paper introduces and analyses, by an exact renormalization decimation procedure, a model of ultradi ffusion on a fractal branching Koch curve with a hierarchical set of biasing terms { η i }.At fixed point η * 0=0, two new crossovers for the dynamical transitions are found. At another fixed point η * 0=W 0 , the decay of the autocorrelation function will change from the power law into the exponential case,where W 0 is the first stage of energy barriers { W i } distributed in a hierarchical way on the fractal curve.