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Register a new userEffect of correlated noise on quasi-1D diffusion
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Single-file diffusion (SFD) of an infinite one-dimensional chain of interacting particles has a long-time mean-square displacement (MSD) ~t^1/2, independent of the type of inter-particle repulsive interaction. This behavior is also observed in finite-size chains, although only for certain intervals of time t depending on the chain length L, followed by the ~t for t->infinity, as we demonstrate for a closed circular chain of diffusing interacting particles. Here we show that spatial correlation of noise slows down SFD and can result, depending on the amount of correlated noise, in either subdiffusive behavior ~t^alpha, where 0<alpha<1/2, or even in a total suppression of diffusion (in the limit N-> infinity). Spatial correlation can explain the subdiffusive behavior in recent SFD experiments in circular channels.
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We consider driven many-particle models which have a phase transition between an active and an absorbing phase. Like previously studied models, we have particle conservation, but here we introduce an additional symmetry - when two particles interact, we give them stochastic kicks which conserve center of mass. We find that the density fluctuations in the active phase decay in the fastest manner possible for a disordered isotropic system, and we present arguments that the large scale fluctuations are determined by a competition between a noise term which generates fluctuations, and a deterministic term which reduces them. Our results may be relevant to shear experiments and may further the understanding of hyperuniformity which occurs at the critical point.
Starting from our recent chemical master equation derivation of the model of an autocatalytic reaction-diffusion chemical system with reactions $U+2V {stackrel {lambda_0}{rightarrow}}~ 3 V;$ and $V {stackrel {mu}{rightarrow}}~P$, $U {stackrel { u}{rightarrow}}~ Q$, we determine the effects of intrinsic noise on the momentum-space behavior of its kinetic parameters and chemical concentrations. We demonstrate that the intrinsic noise induces $n rightarrow n$ molecular interaction processes with $n geq 4$, where $n$ is the number of molecules participating of type $U$ or $V$. The momentum dependences of the reaction rates are driven by the fact that the autocatalytic reaction (inelastic scattering) is renormalized through the existence of an arbitrary number of intermediate elastic scatterings, which can also be interpreted as the creation and subsequent decay of a three body composite state $sigma = phi_u phi_v^2$, where $phi_i$ corresponds to the fields representing the densities of $U$ and $V$. Finally, we discuss the difference between representing $sigma$ as a composite or an elementary particle (molecule) with its own kinetic parameters. In one dimension we find that while they show markedly different behavior in the short spatio-temporal scale, high momentum (UV) limit, they are formally equivalent in the large spatio-temporal scale, low momentum (IR) regime. On the other hand in two dimensions and greater, due to the effects of fluctuations, there is no way to experimentally distinguish between a fundamental and composite $sigma$. Thus in this regime $sigma$ behave as an entity unto itself suggesting that it can be effectively treated as an independent chemical species.
The Rouse-Zimm equation for the position vectors of beads mapping the polymer is generalized by taking into account the viscous aftereffect and the hydrodynamic noise. For the noise, the random fluctuations of the hydrodynamic tensor of stresses are responsible. The preaveraging of the Oseen tensor for the nonstationary Navier-Stokes equation allowed us to relate the time correlation functions of the Fourier components of the bead position to the correlation functions of the hydrodynamic field created by the noise. The velocity autocorrelation function of the center of inertia of the polymer coil is considered in detail for both the short and long times when it behaves according to the t^(-3/2) law and does not depend on any polymer parameters. The diffusion coefficient of the polymer is close to that from the Zimm theory, with corrections depending on the ratio between the size of the bead and the size of the whole coil.
We propose a generalization of the Ornstein-Uhlenbeck process in 1+1 dimensions which is the product of a temporal Ornstein-Uhlenbeck process with a spatial one and has exponentially decaying autocorrelation. The generalized Langevin equation of the process, the corresponding Fokker-Planck equation, and a discrete integral algorithm for numerical simulation is given. The process is an alternative to a recently proposed spatiotemporal correlated model process [J. Garcia-Ojalvo et al., Phys. Rev. A 46, 4670 (1992)] for which we calculate explicitely the hitherto not known autocorrelation function in real space.
Reaction-diffusion systems which include processes of the form A+A->A or A+A->0 are characterised by the appearance of `imaginary multiplicative noise terms in an effective Langevin-type description. However, if `real as well as `imaginary noise is present, then competition between the two could potentially lead to novel behaviour. We thus investigate the asymptotic properties of the following two `mixed noise reaction-diffusion systems. The first is a combination of the annihilation and scattering processes 2A->0, 2A->2B, 2B->2A, and 2B->0. We demonstrate (to all orders in perturbation theory) that this system belongs to the same universality class as the single species annihilation reaction 2A->0. Our second system consists of competing annihilation and fission processes, 2A->0 and 2A->(n+2)A, a model which exhibits a transition between active and absorbing phases. However, this transition and the active phase are not accessible to perturbative methods, as the field theory describing these reactions is shown to be non-renormalisable. This corresponds to the fact that there is no stationary state in the active phase, where the particle density diverges at finite times. We discuss the implications of our analysis for a recent study of another active / absorbing transition in a system with multiplicative noise.
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