scholarly journals A lattice Gas Model for Generic One-Dimensional Hamiltonian Systems

2021 ◽  
Vol 183 (1) ◽  
Author(s):  
J. Schmidt ◽  
G. M. Schütz ◽  
H. van Beijeren
Keyword(s):  
Lattice Gas ◽  
Scaling Function ◽  
Hamiltonian Dynamics ◽  
Exclusion Process ◽  
Universality Class ◽  
Lattice Gas Model ◽  
Dynamical Exponent ◽  
One Dimensional ◽  
Sound Modes ◽  
Order Of Magnitude

AbstractWe present a three-lane exclusion process that exhibits the same universal fluctuation pattern as generic one-dimensional Hamiltonian dynamics with short-range interactions, viz., with two sound modes in the Kardar-Parisi-Zhang (KPZ) universality class (with dynamical exponent $$z=3/2$$ z = 3 / 2 and symmetric Prähofer-Spohn scaling function) and a superdiffusive heat mode with dynamical exponent $$z=5/3$$ z = 5 / 3 and symmetric Lévy scaling function. The lattice gas model is amenable to efficient numerical simulation. Our main findings, obtained from dynamical Monte-Carlo simulation, are: (i) The frequently observed numerical asymmetry of the sound modes is a finite time effect. (ii) The mode-coupling calculation of the scale factor for the 5/3-Lévy-mode gives at least the right order of magnitude. (iii) There are significant diffusive corrections which are non-universal.

Diffusion simulation with a deterministic one-dimensional lattice-gas model

1992 ◽  
Vol 68 (3-4) ◽  
pp. 563-573 ◽  
Author(s):  
Y. H. Qian ◽  
D. d'Humi�res ◽  
P. Lallemand
Keyword(s):  
Lattice Gas ◽  
Lattice Gas Model ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Diffusion Simulation

Theory of Ionic Diffusion Across Material Interfaces

1992 ◽  
Vol 293 ◽  
Author(s):  
M. Balkanski ◽  
I. Nachev ◽  
J. Deppe ◽  
R. F. Wallis
Keyword(s):  
Energy Barrier ◽  
Lattice Gas ◽  
Lattice Gas Model ◽  
Ionic Diffusion ◽  
Intermediate Step ◽  
Material Interfaces ◽  
Linear Diffusion ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Self Consistent

AbstractIon diffusion across material interfaces is considered in a sequence of approximations with increasing complexity. First, the one-dimensional lattice gas model of particle diffusion is generalized to include a finite width interface region, and the possible existence of an energy barrier at the interface. Overvoltage measurements on InSe, and dielectric loss measurements on B2O3 - 0.5Li20 - 0.15Li2SO4 are used to determine the field-free hopping rates in the two materials. It is shown that the energy barrier is a dominant parameter. This model is then modified by considering the disorder of the glass structure and the blocking effect resulting from the ion interaction. Next, a more rigorous treatment is presented by solving the Poisson equation with appropriate boundatry conditions, and a self-consistent theory of the ionic diffusion is proposed. To clarify this problem, an intermediate step and two additional models with increasing sophistication are considered: first, the potential φ(x) of the moving charge density n(x) is calculated and it is shown that φ(x) is not negligible. Then, a feed-back is provided by including this potential in the diffusion equation. This treatment is already self-consistent and more realistic but leads to long computations even for the simple one dimensional lattice-gas model. A remedy of this difficulty is proposed whereby the theory is reformulated in order to guarantee from the beginning the self-consistency of the solution of the non-linear diffusion problem. Straightforward extensions to the two-dimensional case are then possible. The results of the computations are illustrated with numerical examples for different values of the physical parameters.

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