TY - JOUR
T1 - Peierls-Boltzmann equation for ballistic deposition
AU - Schwartz, Moshe
AU - Edwards, S. F.
PY - 1998
Y1 - 1998
N2 - We consider nonlinear stochastic field equations. Going over to a Fokker-Planck description, we construct a self-consistent expansion around a model evolution equation. In second order the equation for the two-point function resembles the Peierls-Boltzmann equation for the average number of phonons, but involves also the unknown characteristic frequency function. Within the same expansion we obtain an equation for that function too. The two coupled equations are studied specifically for the case of ballistic deposition. We show how to obtain the exact asymptotic solution of the two coupled nonlinear integral equations obtained in second order. Higher orders are also discussed.
AB - We consider nonlinear stochastic field equations. Going over to a Fokker-Planck description, we construct a self-consistent expansion around a model evolution equation. In second order the equation for the two-point function resembles the Peierls-Boltzmann equation for the average number of phonons, but involves also the unknown characteristic frequency function. Within the same expansion we obtain an equation for that function too. The two coupled equations are studied specifically for the case of ballistic deposition. We show how to obtain the exact asymptotic solution of the two coupled nonlinear integral equations obtained in second order. Higher orders are also discussed.
UR - https://www.scopus.com/pages/publications/4243351811
U2 - 10.1103/PhysRevE.57.5730
DO - 10.1103/PhysRevE.57.5730
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AN - SCOPUS:4243351811
SN - 1063-651X
VL - 57
SP - 5730
EP - 5739
JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
IS - 5
ER -