Diffusion caused by two noises—active and thermal

Abstract

The diusion of colloids inside an active system-e.g. within a living cell or the dynamics of active particles itself (e.g. self-propelled particles) can be modeled through overdamped Langevin equation which contains an additional noise term apart from the usual white Gaussian noise, originating from the thermal environment. The second noise is referred to as 'active noise' as it arises from activity such as chemical reactions. The probability distribution function (PDF or the propagator) in space-time along with moments provides essential information for understanding their dynamical behavior. Here we employ the phase-space path integral method to obtain the propagator, thereby moments and PDF for some possible models for such noise. At first, we discuss the diusion of a free particle driven by active noise. We consider four dierent possible models for active noise, to capture the possible traits of such systems. We show that the PDF for systems driven by noises other than Gaussian noise largely deviates from normal distribution at short to intermediate time scales as a manifestation of out-of-equilibrium state, albeit converges to Gaussian distribution after a long time as a consequence of the central limit theorem. We extend our work to the case of a particle trapped in a harmonic potential and show that the system attains steady state at long time limit. Also, at short time scales, the nature of distribution is dierent for dierent noises, e.g. for particle driven by dichotomous noise, the probability is mostly concentrated near the boundaries whereas a long exponential tail is observed for a particle driven by Poissonian white noise.

Motion of an active particle with dynamical disorder

“…The results are graphically displayed in Fig. 2 and are equivalent to the one observed for the case in a homogeneous environment [53].…”

Reconfiguration, swelling and tagged monomer dynamics of a single polymer chain in Gaussian and non-Gaussian active baths

“…In the presence of an active noise σ(t) [18,[44][45][46][47][48][49], one requires to include the force term into the dynamics, and therefore, Eq. ( 3) modifies to γ ∂ ∂t r(n, t) = µ ∂ 2 r(n, t) ∂n 2 + η(n, t) + σ(n, t).…”

“…Here we consider the the dynamics of a single passive particle in a harmonic potential of the form: U p (x) = λ 2 x 2 p , where the subscript p is used to label a specific (say, p−th) particle (it may be more clear in the context of polymer dynamics). Apart from thermal fluctuations described by η p (t), the particle is driven by the active noise σ p which arises due to the interaction with the active particles present in the surroundings [18,44,47]. In the overdamped limit, the dynamics can be described by the following stochastic equation [46,48,57,58]:…”

Escape of a passive particle from activity-induced energy landscape: Emergence of slow and fast effective diffusion

“…For telegraphic noise driven processes, the pulses are turned on randomly as a Poisson process with an average waiting time τ . Hence, P (f A ) will be non-Gaussian [24,69,70].…”