拓扑稳定高分子态的有效哈密顿量
Effective Hamiltonian of topologically stabilized polymer states
摘要：
拓扑稳定的聚合物构象中观察到的熔体的nonconcatenated聚合物环和皱巴巴的小球，被认为是一个很好的候选人有丝分裂染色体的空间结构的描述。尽管做出了巨大的努力，但能够描述这种系统的微观哈密顿量仍然无法获得。在本文中，我们考虑一个高斯网络-一个系统，一个简单的哈密顿二次在所有的坐标-并表明，通过调整相互作用，可以获得分形平衡构象与任何分形维数之间的2（理想的聚合物链）和3（皱球）。根据我们对现有数值数据的分析，拓扑稳定状态下的单体-单体距离非常符合高斯分布，为支持二次哈密顿模型提供了额外的论据。在数学上，所得到的聚合物构象可以映射到亚扩散分形布朗粒子的轨迹上。作为我们研究的一个副产品，我们提出了分形布朗运动的两个新的连续积分表示。
英文摘要：
Topologically stabilized polymer conformations observed in melts of nonconcatenated polymer rings and crumpled globules, are considered to be a good candidate for the description of the spatial structure of mitotic chromosomes. Despite significant efforts, the microscopic Hamiltonian capable of describing such systems, remains yet inaccessible. In this paper we consider a Gaussian network - a system with a simple Hamiltonian quadratic in all coordinates - and show that by tuning interactions, one can obtain fractal equilibrium conformations with any fractal dimension between 2 (ideal polymer chain) and 3 (crumpled globule). Monomer-to-monomer distances in topologically stabilized states, according to our analysis of available numerical data, fit very well the Gaussian distribution, giving an additional argument in support of the quadratic Hamiltonian model. Mathematically, the resulting polymer conformations can be mapped onto the trajectories of a subdiffusive fractal Brownian particle. As a by-product of our study, two novel continual integral representations of the fractal Brownian motion are proposed.
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