Abstract
We have investigated a lattice gas model consisting of repulsive particles following deterministic dynamics. Two versions of the model are studied. In one case we consider a finite open system in which particles can leave and enter the lattice over the edge. In the other case we use periodic boundary conditions. In both cases the density fluctuations exhibit a 1/f power spectrum. The individual particles behave asymptotically like ordinary random walkers. The collective behavior of these particles shows that due to the deterministic dynamics the particles behave as if they are correlated in time. We have numerically investigated the power spectrum of the density fluctuations, the lifetime distribution, and the spatial correlation function. We discuss the appropriate Langevin-like diffusion equation which can reproduce our numerical findings. Our conclusion is that the deterministic lattice gases are described by a diffusion equation withoutany bulk noise. The open lattice gas exhibits a crossover behavior as the probability for introducing particles at the edge of the system becomes small. The power spectrum changes from a 1/f to a 1/f 2 spectrum. The diffusive description, proven to be valid for a moderate boundary drive, fails altogether when the drive goes to zero.
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References
J. L. Lebowitz,Physica 140A:232 (1986), and references therein.
D. Forster,Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions (Benjamin, New York, 1975).
T. Hwa and Kadar,Phys. Rev. Lett. 62:1813 (1989).
G. Grinstein, D.-H. Lee, and S. Sachdev,Phys. Rev. Lett. 64:1927 (1990).
Y.-C. Zhang,Physica A 170:1 (1990).
H. J. Jensen,Phys. Rev. Lett. 64:3103 (1990).
J. V. Andersen, H. J. Jensen, and O. G. Mouritsen,Phys. Rev. B 44:439 (1991).
P. Bak, C. Thang, and K. Wiesenfeld,Phys. Rev. Lett. 59:381 (1987).
H. J. Jensen, K. Christensen, and H. C. Fogedby,Phys. Rev. B 40:7425 (1989).
S. H. Liu,Phys. Rev. B 16:4218 (1977).
P. Duta and P. M. Horn,Rev. Mod. Phys. 53:497 (1981).
H. J. Jensen,Physica Scripta 43:593 (1991).
R. N. Bracewell,The Fourier Transform and Its Applications (McGraw-Hill, New York, 1986).
G. Grinstein, T. Hwa, and H. J. Jensen,Phys. Rev. A 45:R559 (1992).
L. Jacobs and C. Rebbi,J. Comp. Phys. 41:203 (1981).
P. M. Morse and H. Feshbach,Methods of Theoretical Physics (McGraw-Hill, New York, 1953).
G. D. Mahan,Many-Particle Physics (Plenum Press, New York, 1990).
P. Duchateau and D. W. Zachmann,Partial Differential Equations (McGraw-Hill, New York, 1986).
S. O. Rice, inSelected Papers on Noise and Stochastic Processes, N. Wax, ed. (Dover, New York, 1954).
H. C. Fogedbyet al., Mod. Phys. Lett. B 5:1837 (1991).
D. K. C. MacDonald,Noise and Fluctuations: An Introduction (Wiley, New York, 1962).
M. Abramowitz and I. A. Stegun,Handbook of Mathematical Functions (Dover, New York, 1972).
I. S. Gradshteyn and I. M. Ryzhik,Table of Integrals, Series, and Products (Academic Press, New York, 1980).
H. J. Jensen,Mod. Phys. Lett. 5:625 (1991).
H. E. Stanley,Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, Oxford, 1971).
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Fiig, T., Jensen, H.J. Diffusive description of lattice gas models. J Stat Phys 71, 653–682 (1993). https://doi.org/10.1007/BF01058441
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DOI: https://doi.org/10.1007/BF01058441