Generalized Elastic Model yields Fractional Langevin Equation

Abstract

Starting from a generalized elastic model which accounts for the stochastic motion of several physical systems such as membranes, (semi)flexible polymers and fluctuating interfaces among others, we derive the fractional Langevin equation (FLE) for a probe particle in such systems, in the case of thermal initial conditions. We show that this FLE is the only one fulfilling the fluctuation-dissipation (FD) relation within a new family of fractional Brownian motion (FBM) equations. The FLE for the time-dependent fluctuations of the donor-acceptor distance in a protein, is shown to be recovered. When the system starts from non-thermal conditions, the corresponding FLE, which does not fulfill FD relation, is derived.

References in corpus (2)

• Langevin formulation for single-file diffusion
• Universal width distributions in non-Markovian Gaussian processes

Cited by in corpus (5)

• Anomalous transport in the crowded world of biological cells
• First Passage Times for a Tracer Particle in Single File Diffusion and Fractional Brownian Motion
• Correlations in a Generalized Elastic Model: Fractional Langevin Equation Approach
• Unusual Response to a Localized Perturbation in a Generalized Elastic Model
• Generalized Fokker-Planck equation and its solution for linear non-Markovian Gaussian systems