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Title:
Statistical physics of topological polymers studied through quaternions
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Abstract:
Polymers with various topological structures are recently synthesized in chemistry such as double-ring polymers, polymers of theta curves and those of complete bipartite graphs. We call them topological polymers. By generating random walks with an algorithm making use of quaternions we study statistical and dynamical properties of topological polymers. For instance, we show that the ratio of the hydrodynamic radius to the gyration radius of a given polymer increases as the topology becomes more complex. We suggest that the ratio can be measured in experiments. Here we remark that the method of quaternions is closely related to equilateral polygons in symplectic geometry.
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