Dynamically emergent correlations in a Brownian gas with diffusing diffusivity

Abstract

We study a gas of $N$ Brownian particles in the presence of a common stochastic diffusivity $D(t)=B^2(t)$, where $B(t)$ represents a one-dimensional Brownian motion at time $t$. Starting from all the particles localized at the origin, the gas expands with a ballistic scaling $x\sim t$. We show that because of the common stochastic diffusivity, the expanding gas gets dynamically correlated, and the joint probability density function of the position of the particles has a CIID structure that was recently found in several other systems. The special structure allows us to compute the average density profile of the gas, extreme and order statistics, gap distribution between successive particles, and the full counting statistics (FCS) that describes the probability density function (PDF) $H(\kappa ,t)$ of the fraction of particles $\kappa$ in a given region $[-L,L]$. Interestingly, the position fluctuation of the central particles and the average density profiles are described by the same scaling function. The PDF describing the FCS has an essential singularity near $\kappa =0$, indicating the presence of particles inside the box $[-L,L]$ at all times. Near the upper limit $\kappa =1$, the scaling function $H(\kappa ,t)$ has a rather unusual behavior: $H(\kappa ,t)\sim (1-\kappa {)}^{\beta (t)}$ where the exponent $\beta (t)$ changes continuously with time. At early times $\beta (t)$ is negative, indicating a divergence of $H(\kappa ,t)$ as $\kappa \to 1$, whereas $\beta (t)$ becomes positive for $t>t_c$ where $t_c$ is computed exactly. Thus, as a function of $t$, the FCS exhibits an interesting shape transition. We also obtain the PDFs of the first-passage time to a given position $x$ and first-exit time from a box $[-L,L]$, by any one of the particles, and find that both PDFs are described by the same scaling function.

31 pages, 11 figures

References in corpus (26)

• Persistence and First-Passage Properties in Non-equilibrium Systems
• Brownian yet non-Gaussian diffusion: from superstatistics to subordination of diffusing diffusivities
• "Diffusing diffusivity": A model for anomalous and "anomalous yet Brownian" diffusion
• Extreme value statistics of correlated random variables: a pedagogical review
• Diffusion-limited reactions in dynamic heterogeneous media
• Packets of Diffusing Particles Exhibit Universal Exponential Tails
• Mortality, Redundancy, and Diversity in Stochastic Search
• A model of non-Gaussian diffusion in heterogeneous media
• Extreme statistics and spacing distribution in a Brownian gas correlated by resetting
• Active Brownian Motion with Directional Reversals
• First passage statistics for diffusing diffusivity
• Universal spectral features of different classes of random diffusivity processes
• A unifying approach to first-passage time distributions in diffusing diffusivity and switching diffusion models
• Maximum of N Independent Brownian Walkers till the First Exit From the Half Space
• Exact extreme, order and sum statistics in a class of strongly correlated system
• Large Deviation in Continuous Time Random Walks
• Dynamically emergent correlations between particles in a switching harmonic trap
• Exact first-passage time distributions for three random diffusivity models
• Statistical properties of single-file diffusion front
• Crowding at the Front of the Marathon Packs
• Exact distributions of cover times for $N$ independent random walkers in one dimension
• Dynamically emergent correlations in bosons via quantum resetting
• Noninteracting particles in a harmonic trap with a stochastically driven center
• Large Deviations in Switching Diffusion: from Free Cumulants to Dynamical Transitions
• Exact height distribution in one-dimensional Edwards-Wilkinson interface with diffusing diffusivity
• Target search by active particles

Cited by in corpus (3)

• Dynamically emergent correlations in Brownian particles subject to simultaneous non-Poissonian resetting protocols
• Emerging correlations between diffusing particles evolving via simultaneous resetting with memory
• Experimental evidence for strong emergent correlations between particles in a switching trap