Dynamics of switching processes: general results and applications to intermittent active motion

TL;DR

This paper develops a general framework to analyze systems with switching dynamics, deriving exact expressions for fluctuations and effective diffusion, and applies it to active particles exhibiting intermittent motion, revealing complex behaviors confirmed by simulations.

Contribution

It provides a novel, exact analytical approach to characterize fluctuations and diffusion in switching dynamical systems, with explicit examples for active particles.

Findings

Position probability density shows rich behaviors due to intermittency

Explicit formulas for spatial cumulants are derived

Numerical simulations validate theoretical results

Abstract

Systems switching between different dynamical phases is an ubiquitous phenomenon. The general understanding of such a process is limited. To this end, we present a general expression that captures fluctuations of a system exhibiting a switching mechanism. Specifically, we obtain an exact expression of the Laplace-transformed characteristic function of the particle's position. Then, the characteristic function is used to compute the effective diffusion coefficient of a system performing intermittent dynamics. Further, we employ two examples: 1) Generalized run-and-tumble active particle, and 2) an active particle switching its dynamics between generalized active run-and-tumble motion and passive Brownian motion. In each case, explicit computations of the spatial cumulants are presented. Our findings reveal that the particle's position probability density function exhibit rich behaviours due to intermittent activity. Numerical simulations confirm our findings.