Evolution of terrace-width distributions on vicinal surfaces: Fokker-Planck derivation of the generalized Wigner surmise.
We use a Fokker-Planck equation to justify the generalization of the Wigner surmise for the energy-level spacing in quantum systems to the simple expression for the equilibrium terrace-width distribution of steps--with arbitrary-strength repulsions--on a vicinal surface, taking advantage of analogies to one-dimensional models of interacting, spinless fermions. This approach leads to an analytic description of the evolution toward equilibrium of steps from several experimentally relevant initial distributions: step bunches, perfect cleaved crystals, and prequench equilibrated distributions at different temperatures.
Pimpinelli
Alberto
A
Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA. alpimpin@univ-bpclermont.fr
Gebremariam
Hailu
H
Einstein
T L
TL