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摘要翻译：
本文研究了自由连接随机链在一定粘性介质中的恒温波动动力学问题。链被看作是一个小粒子系统，它们执行布朗运动，并受到严格的约束，这些约束禁止链的断裂。为了简单起见，粒子之间的所有相互作用都被关闭了，维数被限制在两个。利用路径积分方法，通过在路径积分中插入适当的Dirac-delta函数，解决了描述链在成为连续系统的极限上的涨落的问题。结果表明，脉动链在时间演化过程中可能出现的构象的概率分布与场论的配分函数相一致，场论是非线性sigma模型在二维的推广。在半经典近似下，明确地计算了环形链中珠子位置相关函数的概率分布和生成泛函。
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英文标题：
《A path integral approach to the dynamics of a random chain with rigid
constraints》
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作者：
Franco Ferrari, Jaroslaw Paturej, Thomas A. Vilgis
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最新提交年份：
2008
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
In this work the dynamics of a freely jointed random chain which fluctuates at constant temperature in some viscous medium is studied. The chain is regarded as a system of small particles which perform a brownian motion and are subjected to rigid constraints which forbid the breaking of the chain. For simplicity, all interactions among the particles have been switched off and the number of dimensions has been limited to two. The problem of describing the fluctuations of the chain in the limit in which it becomes a continuous system is solved using a path integral approach, in which the constraints are imposed with the insertion in the path integral of suitable Dirac delta functions. It is shown that the probability distribution of the possible conformations in which the fluctuating chain can be found during its evolution in time coincides with the partition function of a field theory which is a generalization of the nonlinear sigma model in two dimensions. Both the probability distribution and the generating functional of the correlation functions of the positions of the beads are computed explicitly in a semiclassical approximation for a ring-shaped chain.
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PDF链接：
https://arxiv.org/pdf/705.4182
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