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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/7690

Title: Velocity correlations, diffusion and stochasticity in a one-dimensional system
Authors: Balakrishnan, Venkataraman
Bena, Ioana
Van den Broeck, Christian
Issue Date: 2002
Citation: PHYSICAL REVIEW E, 65(3). p. 031102, 1-9
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.
URI: http://hdl.handle.net/1942/7690
DOI: 10.1103/PhysRevE.65.031102
ISI #: 000174548800012
ISSN: 1063-651X
Category: A1
Type: Journal Contribution
Appears in Collections: Research publications

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