Title




Velocity correlations, diffusion and stochasticity in a onedimensional system
 
Author




 
Abstract




We consider the motion of a test particle in a onedimensional system of equalmass point particles. The test particle plays the role of a microscopic piston that separates two hardpoint 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 longtime tail in C(t). The conditions under which this is a t3 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




15393755
[print]
15502376
[online]
 
Volume/pages




65
(2002)
, p. 031102,19
 
ISI




000174548800012
 
Full text (Publisher's DOI)




 
Full text (open access)




 
