Out-of-Equilibrium Step Meandering on a Vicinal Surface

A theory of step meandering on a vicinal surface is developed. At equilibrium, the meander w~[ln(L)]1/2, where L is the lateral extent. During step flow growth, the diffusive repulsion prevails over elasticity. It leads to new scaling laws for the meander w as a function of the interstep distance l, etc. For a weak Schwoebel effect, we find w~l1/4 (at equilibrium w~l). The diffusive repulsion behaves as llnl. Dynamics tend to ``cure'' meandering. At higher growth speed, deterministic roughening intervenes. In this regime we derive general nonlinear equations for interacting ``lines.'' Disordered structures seem to prevail.