RNA扩展矩阵模型的亏格分布
Genus Distributions For Extended Matrix Models Of RNA
摘要：
我们构造并研究了RNA（polymer）折叠的扩展随机矩阵模型。作用于链中所有核苷酸的扰动被添加到RNA配分函数的作用中。研究了这种扰动对配分函数和亏格分布的影响。这种扰动区分了配对和非配对碱基。例如，对于$α= 1$（其中$α$是动作中原始项和扰动项的强度之比），奇数长度的配分函数和亏格分布完全消失。该配分函数和亏格分布对于偶数长度是非零的，其中仅保留具有完全配对碱基的结构。这意味着（i）。属的分布是不同的和（ii）.当$α$在扩展的矩阵模型中接近1时，存在"结构转变"（从"未配对-配对的基本相位"到"完全配对的基本相位"）。我们将扩展的RNA模型的结果与G. Vernizzi，H. Orland和A. Zee在PRL 94，168103（2005）中。
英文摘要：
We construct and study an extended random matrix model of RNA (polymer) folding. A perturbation which acts on all the nucleotides in the chain is added to the action of the RNA partition function. The effect of this perturbation on the partition function and the Genus Distributions is studied. This perturbation distinguishes between the paired and unpaired bases. For example, for $α= 1$ (where $α$ is the ratio of the strengths of the original and perturbed term in the action) the partition function and genus distribution for odd lengths vanish completely. This partition function and the genus distribution is non-zero for even lengths where structures with fully paired bases only remain. This implies that (i). the genus distributions are different and (ii). there is a ``structural transition'' (from an ``unpaired-paired base phase'' to a ``completely paired base phase'') as $α$ approaches 1 in the extended matrix models. We compare the results of the extended RNA model with the results of G. Vernizzi, H. Orland and A. Zee in PRL 94, 168103(2005).
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