Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2002-02-14
Phys. Rev. E. 65, 015102(R) (2002)
Physics
Condensed Matter
Statistical Mechanics
5 pages, no figure
Scientific paper
10.1103/PhysRevE.65.015102
We present a formalism to derive the stochastic differential equations (SDEs) for several solid-on-solid growth models. Our formalism begins with a mapping of the microscopic dynamics of growth models onto the particle systems with reactions and diffusion. We then write the master equations for these corresponding particle systems and find the SDEs for the particle densities. Finally, by connecting the particle densities with the growth heights, we derive the SDEs for the height variables. Applying this formalism to discrete growth models, we find the Edwards-Wilkinson equation for the symmetric body-centered solid-on-solid (BCSOS) model, the Kardar-Parisi-Zhang equation for the asymmetric BCSOS model and the generalized restricted solid-on-solid (RSOS) model, and the Villain--Lai--Das Sarma equation for the conserved RSOS model. In addition to the consistent forms of equations for growth models, we also obtain the coefficients associated with the SDEs.
Kim Doochul
Park Jeong-Man
Park Su-Chan
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