The Motion of a Tagged Particle in the Simple Symmetric Exclusion System on $Z$

Arratia, Richard

doi:10.1214/aop/1176993602

Cited by 213 publications

(248 citation statements)

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“…One can clearly see that two different mecanisms are at stake: the green circles which represent systems of high densities (ρ ≈ 533 m −1 ), which are associated to strongly interacting particles, can be easily distinguished from the red squares which represent systems with lower densities (ρ ≈ 100 and 33 m −1 ), thus weakly interacting particles. Formula (19) seems in good agreement with the transition times of weakly interacting systems whereas formula (20) fits the values of τ ball for strongly interacting ones.…”

Section: Crossover Timesmentioning

confidence: 64%

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Single-file diffusion of particles with long-range interactions: Damping and finite-size effects

2011

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We study the Single File Diffusion (SFD) of a cyclic chain of particles that cannot cross each other, in a thermal bath, with long ranged interactions, and arbitrary damping. We present simulations that exhibit new behaviors specifically associated to systems of small number of particles and to small damping. In order to understand those results, we present an original analysis based on the decomposition of the particles motion in the normal modes of the chain. Our model explains all dynamic regimes observed in our simulations, and provides convincing estimates of the crossover times between those regimes.

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Section: Crossover Timesmentioning

confidence: 64%

“…In the thermodynamic limit (infinite systems with finite density ρ), for overdamped dynamics with hard core interactions, several analytical models [17][18][19][20][21] predict that at long times, the mean square displacement of a particle of mass m grows as F H √ t with the mobility F H given by…”

Section: Introductionmentioning

confidence: 99%

Single-file diffusion of particles with long-range interactions: Damping and finite-size effects

2011

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“…(13). The tagged particle PDF for particle 2 ρ 2 (x 2 , t| x 0 ) = x2 −∞ dx 1 P( x, t| x 0 ) is obtained by the replacements (16). We point out that Eq.…”

Section: Tagged Particle Pdfmentioning

confidence: 99%

“…3 we illustrate the results for the tagged particle PDFs as given in Eq. (16). We compare to stochastic simulations using a new stochastic algorithm described in Appendix A.…”

Section: Tagged Particle Pdfmentioning

confidence: 99%

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Single-file dynamics with different diffusion constants

Ambjörnsson

Lizana²,

Lomholt

et al. 2008

The Journal of Chemical Physics

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We investigate the single-file dynamics of a tagged particle in a system consisting of N hardcore interacting particles (the particles cannot pass each other) which are diffusing in a one-dimensional system where the particles have different diffusion constants. For the two particle case an exact result for the conditional probability density function (PDF) is obtained for arbitrary initial particle positions and all times. The two-particle PDF is used to obtain the tagged particle PDF. For the general N -particle case (N large) we perform stochastic simulations using our new computationally efficient stochastic simulation technique based on the Gillespie algorithm. We find that the mean square displacement for a tagged particle scales as the square root of time (as for identical particles) for long times, with a prefactor which depends on the diffusion constants for the particles; these results are in excellent agreement with very recent analytic predictions in the mathematics literature.

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Diffusive limit of a tagged particle in asymmetric simple exclusion processes

Sethuraman

Varadhan

Yau

2000

Comm Pure Appl Math

101

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The study of equilibrium fluctuations of a tagged particle in finite-range simple exclusion processes has a long history. The belief is that the scaled centered tagged particle motion behaves as some sort of homogenized random walk. In fact, invariance principles have been proved in all dimensions d ≥ 1 when the single particle jump rate is unbiased, in d ≥ 3 when the jump rate is biased, and in d = 1 when the jump rate is in addition nearest-neighbor.The purpose of this article is to give some partial results in the open cases in d ≤ 2. Namely, we show the tagged particle motion is "diffusive" in the sense that upper and lower bounds are given for the tagged particle variance at time t on order O(t) in d = 2 when the jump rate is biased, and also in d = 1 when in addition the jump rate is not nearest-neighbor. Also, a characterization of the tagged particle variance is given. The main methods are in analyzing H −1 norm variational inequalities.

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The Motion of a Tagged Particle in the Simple Symmetric Exclusion System on $Z$

Cited by 213 publications

References 0 publications

Single-file diffusion of particles with long-range interactions: Damping and finite-size effects

Single-file diffusion of particles with long-range interactions: Damping and finite-size effects

Single-file dynamics with different diffusion constants

Diffusive limit of a tagged particle in asymmetric simple exclusion processes

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