Complementary mode analyses between sub- and superdiffusion

Several subdiffusive stochastic processes in nature, e.g., the motion of a tagged monomer in polymers, the height fluctuation of interfaces, particle dynamics in single-file diffusion, etc., can be described rigorously or approximately by the superposition of various modes whose relaxation times are broadly distributed. In this paper, we propose a mode analysis generating superdiffusion, which is paired with or complementary to subdiffusion. The key point in our discussion lies in the identification of a pair of conjugated variables, which undergo sub- and superdiffusion, respectively. We provide a simple interpretation for the sub- and superdiffusion duality for these variables using the language of polymer physics. The analysis also suggests the usefulness of looking at the force fluctuation in experiments, where a polymer is driven by a constant velocity.