Correlations in a Generalized Elastic Model: Fractional Langevin Equation Approach

Abstract

The Generalized Elastic Model (GEM) provides the evolution equation which governs the stochastic motion of several many-body systems in nature, such as polymers, membranes, growing interfaces. On the other hand a probe (\emph{tracer}) particle in these systems performs a fractional Brownian motion due to the spatial interactions with the other system's components. The tracer's anomalous dynamics can be described by a Fractional Langevin Equation (FLE) with a space-time correlated noise. We demonstrate that the description given in terms of GEM coincides with that furnished by the relative FLE, by showing that the correlation functions of the stochastic field obtained within the FLE framework agree to the corresponding quantities calculated from the GEM. Furthermore we show that the Fox $H$-function formalism appears to be very convenient to describe the correlation properties within the FLE approach.

References in corpus (2)

• Generalized Elastic Model yields Fractional Langevin Equation
• Langevin formulation for single-file diffusion

Cited by in corpus (4)

• Anomalous transport in the crowded world of biological cells
• Unusual Response to a Localized Perturbation in a Generalized Elastic Model
• Interacting single-file system: Fractional Langevin formulation versus diffusion-noise approach
• Generalized Fokker-Planck equation and its solution for linear non-Markovian Gaussian systems