Complementary mode analyses between sub- and superdiffusion

Abstract

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.

Negative friction memory induces persistent motion

“…If the dynamics of a diffusing particle is coupled to other degrees of freedom, memory effects occur, and the particle dynamics becomes non-Markovian [1,2]. Examples include the diffusion of a tracer bead in viscoleastic [3][4][5][6] and heterogeneous [7,8] media, polymer dynamics [9][10][11][12][13] and dynamics in rough energy landscapes [14][15][16]. Furthermore, many systems far from equilibrium, such as self-propelled particles [17][18][19] or passive tracer particles in active media [20][21][22], exhibit non-Markovian dynamics.…”

Inferring Active Noise Characteristics from the Paired Observations of Anomalous Diffusion

“…As a simple example, consider a tagged monomer in a Rouse polymer. The analysis based on the generalized Langevin equation (GLE) leads to the superdiffusion with α(p)=3/2 [26,27]. Since the position displacement and the momentum transfer are conjugate to each other with respect to Hamiltonian, one expects that there may be some relation between α(x) and α(p).…”

“…Since the position displacement and the momentum transfer are conjugate to each other with respect to Hamiltonian, one expects that there may be some relation between α(x) and α(p). Indeed, from the analysis of the GLE with the fluctuation–dissipation relation, one can verify the following sum relation generally holds in thermal equilibrium [26]:α(x)+α(p)=2.…”

Dynamics of networks in a viscoelastic and active environment

“…In eqn (11) Equations (11)-(13) allow to study different dynamical properties of the macromolecules. Here we concentrate on the monomeric displacement,…”

“…Modern experiments on the dynamics of biopolymers in a crowded active bath (such as motion of chromosomal loci in bacteria) have demonstrated striking features of the macromolecular systems in the out-of-equilibrium environments. 1,2 Indeed, as has been shown in a rapidly growing series of recent studies, [3][4][5][6][7][8][9][10][11][12][13][14][15][16] the behavior of macromolecules in the active and crowded environments differs tremendously from that of the polymers in a usual thermal bath. 17 In particular, the activity leads typically to a swelling of macromolecules, 5,8 the dynamics is drastically enhanced yielding a change of scalings, 4,10,11 and the kinetics of the intramolecular reactions is facilitated.…”