Scaling of ballistic deposition from a Langevin equation.
An exact lattice Langevin equation is derived for the ballistic deposition model of surface growth. The continuum limit of this equation is dominated by the Kardar-Parisi-Zhang (KPZ) equation at all length and time scales. For a one-dimensional substrate the solution of the exact lattice Langevin equation yields the KPZ scaling exponents without any extrapolation. For a two-dimensional substrate the scaling exponents are different from those found from computer simulations. This discrepancy is discussed in relation to analytic approaches to the KPZ equation in higher dimensions.
Haselwandter
Christoph A
CA
The Blackett Laboratory, Imperial College, London SW7 2BW, United Kingdom.
Vvedensky
Dimitri D
DD