Publication
Title
Velocity correlations, diffusion and stochasticity in a one-dimensional system
Author
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.
Language
English
Source (journal)
Physical review : E : statistical, nonlinear, and soft matter physics / American Physical Society. - Melville, N.Y., 2001 - 2015
Publication
Melville, N.Y. : American Physical Society, 2002
ISSN
1539-3755 [print]
1550-2376 [online]
Volume/pages
65(2002), p. 031102,1-9
ISI
000174548800012
Full text (Publishers DOI)
Full text (open access)
UAntwerpen
Faculty/Department
Research group
Publication type
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identification
Creation 08.10.2008
Last edited 08.03.2017
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