Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userInteracting Random Walkers and Non-Equilibrium Fluctuations
208
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We introduce a model of interacting Random Walk, whose hopping amplitude depends on the number of walkers/particles on the link. The mesoscopic counterpart of such a microscopic dynamics is a diffusing system whose diffusivity depends on the particle density. A non-equilibrium stationary flux can be induced by suitable boundary conditions, and we show indeed that it is mesoscopically described by a Fourier equation with a density dependent diffusivity. A simple mean-field description predicts a critical diffusivity if the hopping amplitude vanishes for a certain walker density. Actually, we evidence that, even if the density equals this pseudo-critical value, the system does not present any criticality but only a dynamical slowing down. This property is confirmed by the fact that, in spite of interaction, the particle distribution at equilibrium is simply described in terms of a product of Poissonians. For mesoscopic systems with a stationary flux, a very effect of interaction among particles consists in the amplification of fluctuations, which is especially relevant close to the pseudo-critical density. This agrees with analogous results obtained for Ising models, clarifying that larger fluctuations are induced by the dynamical slowing down and not by a genuine criticality. The consistency of this amplification effect with altered coloured noise in time series is also proved.
rate research
Read More
We study a model of bacterial dynamics where two interacting random walkers perform run-and-tumble motion on a one-dimensional lattice under mutual exclusion and find an exact expression for the probability distribution in the steady state. This stationary distribution has a rich structure comprising three components: a jammed component, where the particles are adjacent and block each other; an attractive component, where the probability distribution for the distance between particles decays exponentially; and an extended component in which the distance between particles is uniformly distributed. The attraction between the particles is sufficiently strong that even in the limit where continuous space is recovered for a finite system, the two walkers spend a finite fraction of time in a jammed configuration. Our results potentially provide a route to understanding the motility-induced phase separation characteristic of active matter from a microscopic perspective.
We derive an exact formula for the scaled cumulant generating function of the time-integrated current associated to an arbitrary ballistically transported conserved charge. Our results rely on the Euler-scale description of interacting, many-body, integrable models out of equilibrium given by the generalized hydrodynamics, and on the large deviation theory. Crucially, our findings extend previous studies by accounting for inhomogeneous and dynamical initial states in interacting systems. We present exact expressions for the first three cumulants of the time-integrated current. Considering the non-interacting limit of our general expression for the scaled cumulant generating function, we further show that for the partitioning protocol initial state our result coincides with previous results of the literature. Given the universality of the generalized hydrodynamics, the expression obtained for the scaled cumulant generating function is applicable to any interacting integrable model obeying the hydrodynamic equations, both classical and quantum.
We study a model of interacting run-and-tumble random walkers operating under mutual hardcore exclusion on a one-dimensional lattice with periodic boundary conditions. We incorporate a finite, Poisson-distributed, tumble duration so that a particle remains stationary whilst tumbling, thus generalising the persistent random walker model. We present the exact solution for the nonequilibrium stationary state of this system in the case of two random walkers. We find this to be characterised by two lengthscales, one arising from the jamming of approaching particles, and the other from one particle moving when the other is tumbling. The first of these lengthscales vanishes in a scaling limit where the continuous-space dynamics is recovered whilst the second remains finite. Thus the nonequilibrium stationary state reveals a rich structure of attractive, jammed and extended pieces.
We consider random walkers that deform the medium as they move, enabling a faster motion in regions which have been recently visited. This induces an effective attraction between walkers mediated by the medium, which can be regarded as a space metric, giving rise to a statistical mechanics toy model either for gravity, motion through deformable matter or adaptable geometry. In the strong-deformability regime, we find that diffusion is initially described by the porous medium equation, thus yielding subdiffusive behavior of an initially localized cloud of particles. Indeed, while the average width of a single cloud will sustain a $sigmasim t^{1/2}$ growth, the combined width of the whole ensemble will grow like $sigmasim t^{1/3}$ in a certain time regime. This difference can be accounted for by the strong correlations between the particles, which we explore indirectly through the fluctuations of the center of mass of the cloud and the expected value of the experienced density, defined as the average density measured by the particles themselves.
We report the study of a new experimental granular Brownian motor, inspired to the one published in [Phys. Rev. Lett. 104, 248001 (2010)], but different in some ingredients. As in that previous work, the motor is constituted by a rotating pawl whose surfaces break the rotation-inversion symmetry through alternated patches of different inelasticity, immersed in a gas of granular particles. The main novelty of our experimental setup is in the orientation of the main axis, which is parallel to the (vertical) direction of shaking of the granular fluid, guaranteeing an isotropic distribution for the velocities of colliding grains, characterized by a variance $v_0^2$. We also keep the granular system diluted, in order to compare with Boltzmann-equation-based kinetic theory. In agreement with theory, we observe for the first time the crucial role of Coulomb friction which induces two main regimes: (i) rare collisions (RC), with an average drift $ < omega > sim v_0^3$, and (ii) frequent collisions (FC), with $ < omega > sim v_0$. We also study the fluctuations of the angle spanned in a large time interval, $Delta theta$, which in the FC regime is proportional to the work done upon the motor. We observe that the Fluctuation Relation is satisfied with a slope which weakly depends on the relative collision frequency.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
