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 (8)

• Fractional Langevin equation
• Persistence exponents for fluctuating interfaces
• The Critical Exponent of the Fractional Langevin Equation is ${\alpha }_c\approx 0.402$
• Fractional Langevin equation to describe anomalous diffusion
• Spatial Persistence of Fluctuating Interfaces
• Anomalous escape governed by thermal 1/f noise
• Langevin formulation for single-file diffusion
• Universal width distributions in non-Markovian Gaussian processes

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