Complementary mode analyses between sub- and super-diffusions

Several sub-diffusive stochastic processes in nature, e.g., motion of tagged monomer in polymers, height fluctuation of interfaces and 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 super-diffusion, which is paired or complementary with that for sub-diffusion. The key point in our discussion lies in the identification of a pair of conjugated variables, which undergoes sub- and super-diffusion, 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 to look at the force fluctuation in experiments, where a polymer is driven by a constant velocity.