FRACTIONAL KINETIC-EQUATION FOR HAMILTONIAN CHAOS
FRACTIONAL KINETIC-EQUATION FOR HAMILTONIAN CHAOS
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DOI：
10.1016/0167-2789(94)90254-2
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发表时间：
1994-09-01
影响因子：
4
通讯作者：
ZASLAVSKY, GM
中科院分区：
文献类型：
--
作者：
ZASLAVSKY, GM
粒子(或流体中的被动粒子)的哈密顿混沌动力学可以用Fokker-Planck-Kolmogorov方程(FFPK)的分数推广来描述，该方程由两个分数临界指数(α，β)定义，分别对应于分布函数的空间和时间导数。提出了一种从第一原理(即从哈密顿量)确定(α，β)的重整化方法。对于自相似输运中的一阶平均位移，得到了反常输运指数Mu=β/α或Mu=β/2α。
Hamiltonian chaotic dynamics of particles (or passive particles in fluids) can be described by a fractional generalization of the Fokker-Planck-Kolmogorov equation (FFPK) which is defined by two fractional critical exponents (alpha, beta) responsible for the space and time derivatives of the distribution function correspondingly. A renormalization method has been proposed to determine (alpha, beta) from the first principles (i.e. from the Hamiltonian). The anomalous transport exponent mu is derived as mu = beta/alpha or mu = beta/2 alpha for the first order mean displacement in self-similar transport.