Survey of roughness by stochastic oscillations

Details Survey of roughness by stochastic oscillations Survey of roughness by stochastic oscillations

2006-10-27

arxiv.org/abs/cond-mat/0610775v2

Physics

Condensed Matter

Statistical Mechanics

8 pages, 4 figures

Scientific paper

In this paper, connections between surface roughness and directed polymers in random medium are studied, when the surface is considered as a directed line undergoing stochastic oscillations. This is performed by studying the influence of a stochastic elastic forcing term $-\kappa y+\eta(s)$, on a particle moving along a rough surface. Two models are proposed and analysed in this way: the random-walk process (RW) in its discrete and continuous form, and a Markovian process via the Ornstein-Uhlenbeck (O-U) process. It is shown that the continuous RW leads to an oscillator equation, via an effective action obeying a KPZ equation which is solved analytically. The O-U process allows to obtain information on the profile of surface for a long size substrate. The analogy with the roughness is achieved by introducing a quantity suited to directed line formalism: the height velocity variation $\partial h/\partial s$.

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