Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2006-03-24
Phys. Rev. E 74, 031105 (2006)
Physics
Condensed Matter
Statistical Mechanics
Scientific paper
10.1103/PhysRevE.74.031105
We study the statistical properties of many Brownian particles under the We study the statistical properties of many Brownian particles under the influence of both a spatially homogeneous driving force and a periodic potential with period $\ell$ in a two-dimensional space. In particular, we focus on two asymptotic cases, $\ell_{\rm int} \ll \ell$ and $\ell_{\rm int} \gg \ell$, where $\ell_{\rm int}$ represents the interaction length between two particles. We derive fluctuating hydrodynamic equations describing the evolution of a coarse-grained density field defined on scales much larger than $\ell$ for both the cases. Using the obtained equations, we calculate the equal-time correlation functions of the density field to the lowest order of the interaction strength. We find that the system exhibits the long-range correlation of the type $r^{-d}$ ($d=2$) for the case $\ell_{\rm int} \gg \ell$, while no such behavior is observed for the case $\ell_{\rm int}\ll \ell$.
Nakamura Takenobu
Sasa Shin-ichi
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