title: Colloidal dynamics over a tilted periodic potential: Nonequilibrium steady-state distributions.
abstract: We report a systematic study of the effects of the external force F on the nonequilibrium steady-state (NESS) dynamics of the diffusing particles over a tilted periodic potential, in which detailed balance is broken due to the presence of a steady particle flux. A tilted two-layer colloidal system is constructed for this study. The periodic potential is provided by the bottom-layer colloidal spheres forming a fixed crystalline pattern on a glass substrate. The corrugated surface of the bottom colloidal crystal provides a gravitational potential field for the top-layer diffusing particles. By tilting the sample at an angle θ with respect to the vertical (gravity) direction, a tangential component of the gravitational force F is applied to the diffusing particles. The measured NESS probability density function P(ss)(x,y) of the particles is found to deviate from the equilibrium distribution P(x,y) to a different extent, depending on the driving or distance from equilibrium. The experimental results are compared with the exact solution of the one-dimensional (1D) Smoluchowski equation and the numerical results of the 2D Smoluchowski equation. From the obtained exact solution of the 1D Smoluchowski equation, we develop an analytical method to accurately extract the 1D potential U(0)(x) from the measured P(ss)(x). This work demonstrates that the tilted periodic potential provides a useful platform for the study of forced barrier-crossing dynamics beyond the Arrhenius-Kramers equation.
authors.affiliation: Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong.
authors.forename: Xiao-guang
authors.initials: XG
authors.lastname: Ma
authors.affiliation: Department of Physics and Center for Complex Systems, National Central University, Chungli, Taiwan 320, R.O.C.|Physics Division, National Center for Theoretical Sciences, Kuang Fu Road 101, Hsinchu, Taiwan 300, R.O.C.
authors.forename: Pik-Yin
authors.initials: PY
authors.lastname: Lai
authors.affiliation: Department of Physics, Oklahoma State University, Stillwater, Oklahoma 74078, USA.
authors.forename: Bruce J
authors.initials: BJ
authors.lastname: Ackerson
authors.affiliation: Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong.
authors.forename: Penger
authors.initials: P
authors.lastname: Tong