Correlation in thermal fluctuations induced by phase-locked hydrodynamic modes.

Abstract

Thermal fluctuations constitute a fundamental equilibrium phenomenon whose spatial and temporal correlations are governed by the relevant scales of molecular collisions. From the continuum point of view, thermal fluctuations in a fluid can be regarded as comprising a multitude of hydrodynamic modes (HMs) with random phases, each one having one degree of freedom. We show that in a two-dimensional fluid channel with the Navier slip boundary condition, in which the HMs are represented by periodic arrays of vortex and antivortex pairs, periodic modulation of the slip boundary condition can selectively suppress noncommensurate HMs while phase lock the remaining eigenmodes. As a result, thermal fluctuations would exhibit mesoscopic-scale spatial correlations, manifest as a spatially varying diffusion constant when evaluated from the fluctuation-dissipation theorem. Good agreement is shown with the molecular dynamics results. Such manifestation of equilibrium collective motion implies that instead of just being an alternative mathematical basis for expressing thermal fluctuations, in mesoscopic systems the HMs may be manipulated to have physical consequences very different from those expected in bulk fluid.