Two-states Brownian particle in a Harmonic Potential

Abstract

We study the behaviour of a Brownian particle in the overdamped regime in the presence of a harmonic potential, assuming its diffusion coefficient to randomly jump between two distinct values. In particular, we characterize the probability distribution of the particle position and provide detailed expressions for the mean square displacement and the kurtosis. We highlight non-Gaussian behaviour even within the long-term limit carried over with an excess of probability both in the central part and in the distribution's tails. Moreover, when one of the two diffusion coefficients assumes the value zero, we provide evidence that the probability distribution develops a cusp. Most of our results are analytical, and corroborated by numerical simulations.

9 pagine, 4 figure

References in corpus (8)

• "Diffusing diffusivity": A model for anomalous and "anomalous yet Brownian" diffusion
• Relaxation Functions of Ornstein-Uhlenbeck Process with Fluctuating Diffusivity
• Rate equations, spatial moments, and concentration profiles for mobile-immobile models with power-law and mixed waiting time distributions
• Brownian non-Gaussian polymer diffusion and queing theory in the mean-field limit
• Polymers critical point originates Brownian non-Gaussian diffusion
• Being Heterogeneous Is Advantageous: Extreme Brownian Non-Gaussian Searches
• Brownian non-Gaussian diffusion of self-avoiding walks
• Being heterogeneous is disadvantageous: Brownian non-Gaussian searches