A lattice Gas Model for Generic One-Dimensional Hamiltonian Systems

We 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 and symmetri...

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Bibliographic Details
Published in:Journal of statistical physics 2021-04, Vol.183 (1), Article 8
Main Authors: Schmidt, J., Schütz, G. M., van Beijeren, H.
Format: Article
Language:English
Subjects:
Analysis
Hamiltonian functions
Lattice vibration
Mathematical and Computational Physics
Mathematical models
Monte Carlo method
Monte Carlo simulation
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Sound
Statistical Physics and Dynamical Systems
Theoretical
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Summary:We 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 and symmetric Prähofer-Spohn scaling function) and a superdiffusive heat mode with dynamical exponent 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.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-021-02709-1