运动聚合物的标度性质
Scaling Properties of a Moving Polymer
摘要：
本文建立了一个本征长度$J$取$(0,\infty)$的运动弱自回避聚合物的SPDE模型。我们的主要结果表明，聚合物的有效半径约为$J^{5/3}$ ;显然，对于大的$J$，聚合物经历拉伸。这与没有时间变量的平衡情形形成对比，在平衡情形中，许多早期的结果表明有效半径近似为$J$。对于这样一个移动的聚合物采取值在$\mathbf{R}^2$，我们提供了一个猜想，有效半径约为$J^{5/4}$。
英文摘要：
We set up an SPDE model for a moving, weakly self-avoiding polymer with intrinsic length $J$ taking values in $(0,\infty)$. Our main result states that the effective radius of the polymer is approximately $J^{5/3}$; evidently for large $J$ the polymer undergoes stretching. This contrasts with the equilibrium situation without the time variable, where many earlier results show that the effective radius is approximately $J$. For such a moving polymer taking values in $\mathbf{R}^2$, we offer a conjecture that the effective radius is approximately $J^{5/4}$.
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