2001/09/03 by V. Balakrishnan, Iosif Bena, I. Bena +1 · 1 citation
Engineering · Materials Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Material Dynamics and Properties #Phase Equilibria and Thermodynamics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.65.031102
22 files, 2 eps figures. Submitted to PRE
arxiv created 2001/09/03 · openalex publication_date 2002/02/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.