Effect of correlated noise on quasi-one-dimensional diffusion

Abstract

Single-file diffusion (SFD) of an infinite one-dimensional chain of interacting particles has a long-time mean-square displacement ∝t(1/2), independent of the type of interparticle 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→∞, 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 ∝tα, where 0<α<1/2, or even in a total suppression of diffusion (in the limit N→∞). Spatial correlation can explain the subdiffusive behavior in recent SFD experiments in circular channels.

Tunable diffusion of magnetic particles in a quasi-one-dimensional channel

“…For φ 55 o , the interaction potential is mainly repulsive and therefore it leads the system into a subdiffusive behavior, where α = 0.5. The scaling W (t) ∝ t 0.5 has been observed experimentally in repulsive interacting particles [37], and was also found from simulations [46,59] and through analytical [62,63] calculations. In this case, the minimum interparticle distance is approximately equal to d ≈ (ρ) −1 ≈ 1.2.…”

“…Furthermore, q1D systems can be used as models for the study of collective phenomena in low dimensional systems, e.g, vortex matter in type-II superconductors [43,44], colloidal particles [45,46] and dusty plasmas. In addition, the mechanisms of ion transport in narrow channels [47] and DNA manipulation using magnetic particles [48,49] can be studied by modelling q1D systems.…”

Single-file and normal diffusion of magnetic colloids in modulated channels

“…W x (t) ∝ t α (with α < 0.5), is also observed. Such a behaviour was also found in experiments with millimetre metallic balls [52] and in numerical simulations [53] taking into account spatial correlated noises.…”

Emerging quasi-0D states at vanishing total entropy of the 1D hard sphere system: A coarse-grained similarity to the car parking problem

“…1, we further compare the third exponent α 3 with the final exponents in the long time limit: the maximum exponent, α max ∞ → 1 (red line), and the minimum, α min ∞ → 0 (blue line). While the maximum exponent is associated with the Goldstone-like diffusion of the 1D chain as a whole [10,12], the 1D particles confined in either a finite box or a harmonic potential will find their equilibrium positions, yielding the almost constant MSD (or the minimum exponent of α min ∞ → 0) [15]. It is thus seen from Fig.…”

“…The MSD has been found to obey the scaling law, ∼ t α , with respect to a time interval t [5-11, 13, 14]. Recent experimental and simulation * frusawa.hiroshi@kochi-tech.ac.jp studies have verified the crossover change of the MSD dependence from normal (α = 1) to single-file (α = 0.5) exponents [7] with an increase of t. Some experiments have also suggested the existence of a third region where the sub-diffusive exponent is further reduced to a long-time asymptote of α < 0.5 [8], and the diminished exponent of α < 0.5 has been reproduced by computer simulations of atomistic models [9][10][11]. Furthermore, it was reported that initial conditions determine the long time limit of the tagged particle dynamics in an infinite 1D channel [14].…”