Title
Velocity correlations, diffusion and stochasticity in a one-dimensional system Velocity correlations, diffusion and stochasticity in a one-dimensional system
Author
Faculty/Department
Faculty of Sciences. Physics
Publication type
article
Publication
Melville, N.Y. :American Physical Society ,
Source (journal)
Physical review : E : statistical, nonlinear, and soft matter physics / American Physical Society. - Melville, N.Y., 2001 - 2015
Volume/pages
65(2002) , p. 031102,1-9
ISSN
1539-3755
1550-2376
ISI
000174548800012
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
We consider the motion of a test particle in a one-dimensional system of equal-mass point particles. The test particle plays the role of a microscopic piston that separates two hard-point gases with different concentrations and arbitrary initial velocity distributions. In the homogeneous case when the gases on either side of the piston are in the same macroscopic state, we compute and analyze the stationary velocity autocorrelation function C(t). Explicit expressions are obtained for certain typical velocity distributions, serving to elucidate in particular the asymptotic behavior of C(t). It is shown that the occurrence of a nonvanishing probability mass at zero velocity is necessary for the occurrence of a long-time tail in C(t). The conditions under which this is a t-3 tail are determined. Turning to the inhomogeneous system with different macroscopic states on either side of the piston, we determine its effective diffusion coefficient from the asymptotic behavior of the variance of its position, as well as the leading behavior of the other moments about the mean. Finally, we present an interpretation of the effective noise arising from the dynamics of the two gases, and thence that of the stochastic process to which the position of any particle in the system reduces in the thermodynamic limit.
Full text (open access)
https://repository.uantwerpen.be/docman/irua/5652a1/8086.pdf
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