• Corpus ID: 4948513

On the Diffusion of Sticky Particles in 1D

@article{Hellier2018OnTD,
  title={On the Diffusion of Sticky Particles in 1D},
  author={Joshua D M Hellier and Graeme J. Ackland},
  journal={arXiv: Statistical Mechanics},
  year={2018}
}
The 1D Ising model is the simplest Hamiltonian-based model in statistical mechanics. The sim- plest interacting particle process is the Symmetric Exclusion Process (SEP), a 1D lattice gas of particles that hop symmetrically and cannot overlap. Combining the two gives a model for sticky particle diffusion, SPM, which is described here. SPM dynamics are based on SEP with short-range interaction, allowing flow due to non-equilibrium boundary conditions. We prove that SPM is also a detailed-balance… 

References

SHOWING 1-10 OF 36 REFERENCES
Large Deviations of a Tracer in the Symmetric Exclusion Process.
TLDR
An exact formula for the cumulant generating function and the large deviation function of X_{t} in the long-time limit is derived and the full statistical properties of the tracer's position are deduced as an important special case.
Single-file diffusion of atomic and colloidal systems: asymptotic laws.
TLDR
The asymptotic behavior of the mean-squared displacement, W(t), is shown to be independent of the nature of interactions for homogeneous systems in the fluid state and the long-time behavior of self-diffusion is determined by short-time and large-scale collective density fluctuations.
Long range correlations for stochastic lattice gases in a non-equilibrium steady state
The author considers a system with a single locally-conserved field ( identical to density) in a slab geometry with different densities maintained at the two surfaces of the slab. On the basis of
Nonequilibrium steady states of stochastic lattice gas models of fast ionic conductors
We investigate theoretically and via computer simulation the stationary nonequilibrium states of a stochastic lattice gas under the influence of a uniform external fieldE. The effect of the field is
Large deviations in single-file diffusion.
We apply macroscopic fluctuation theory to study the diffusion of a tracer in a one-dimensional interacting particle system with excluded mutual passage, known as single-file diffusion. In the case
TOPICAL REVIEW: Nonequilibrium steady states of matrix-product form: a solver's guide
TLDR
The general problem of determining the steady state of stochastic nonequilibrium systems such as those used to model biological transport and traffic flow is considered, and a unified, pedagogical account of the various means by which the statistical mechanical calculations of macroscopic physical quantities are actually performed is presented.
A dynamical monte carlo algorithm for master equations with time-dependent transition rates
A Monte Carlo algorithm for simulating master equations with time-dependent transition rates is described. It is based on a waiting time image, and takes into account that the system can become
Universal large deviations for the tagged particle in single-file motion.
TLDR
Here the exact large deviation function for the tagged particle displacement is computed and it is shown that this is universal, independent of the individual dynamics.
Diffusion Constants near the Critical Point for Time-Dependent Ising Models. I
The diffusion constant of spins in ferromagnets or of molecules in binary mixtures near the critical point is discussed employing a time-dependent Ising model in which spin interactions are replaced
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