Observation-Time-Induced Crossover from Fluctuating Diffusivity

Abstract

A dynamical transition -- seen as a sudden increase in the mean-squared displacement at a characteristic temperature that depends on the observation time -- is widely reported in neutron-scattering experiments and molecular dynamics simulations of hydrated proteins. However, its physical origin remains elusive. We show that fluctuating diffusivity in a Langevin framework leads to an observation-time-induced crossover, where the effective diffusion coefficient exhibits a temperature-dependent transition whose crossover point shifts with observation time. Analytical and numerical analyses reveal the mechanism of this crossover and delineate the conditions under which it emerges. Our findings provide a unified nonequilibrium interpretation for observation-time-induced crossover, and suggest that the protein dynamical transition can be viewed as an instance of this general crossover mechanism.

Figures (2)

• Figure 1: Particle trajectory $x(t)$ and corresponding time-dependent diffusion coefficient $D(t)$ in the DWCDD model.
• Figure 2: Temperature-dependent effective diffusion coefficient for different observation times in the DWCDD model. Symbols indicate simulation results, dashed lines represent the initial and equilibrium diffusion coefficients, and solid lines show the theoretical prediction given by Eq. \ref{['eq:D_eff']}. Inset: linear-scale zoom around $T<0.2$.