变形统计系综的自相似度
Self-similarity degree of deformed statistical ensembles
摘要：
我们考虑自相似统计系综与相空间的体积是不变的变形下，挤压（扩大）的坐标和扩大（挤压）的动量。相关的概率分布函数被证明具有离散对称性关于流形作用的杰克逊导数是一个齐次函数的自相似度$q$固定的条件下的不变性$(n+1)$倍行动的扩张算子有关。在微变形相空间中，我们发现齐次函数在$n=0$处具有线性相关性，而在$n=1$处自相似度等于黄金平均，在极限$n\to\infty$处自相似度等于$q\to n$.齐次函数的伸缩性降低了自相似度$q$在$n>0$。
英文摘要：
We consider self-similar statistical ensembles with the phase space whose volume is invariant under the deformation that squeezes (expands) the coordinate and expands (squeezes) the momentum. Related probability distribution function is shown to possess a discrete symmetry with respect to manifold action of the Jackson derivative to be a homogeneous function with a self-similarity degree $q$ fixed by the condition of invariance under $(n+1)$-fold action of the dilatation operator related. In slightly deformed phase space, we find the homogeneous function is defined with the linear dependence at $n=0$, whereas the self-similarity degree equals the gold mean at $n=1$, and $q\to n$ in the limit $n\to\infty$. Dilatation of the homogeneous function is shown to decrease the self-similarity degree $q$ at $n>0$.
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