Exploring the Unstable Modes Dynamics by the Lattice Schrodinger Functional

We analyze the problem of the Nielsen-Olesen unstable modes in the $SU(2)$ lattice gauge theory by means of a recently introduced gauge-invariant effective action. We perform numerical simulations in the case of a constant Abelian chromomagnetic field. We find that for lattice sizes above a certain critical length the density of effective action shows a behaviour compatible with the presence of the unstable modes.