Non-perturbative Solution of the Unitary, $N$-Orbital Anderson Model

The mobility edge is extracted from a non-perturbative analysis of F. Wegner’s real matrix ensemble (RME), $N$-orbital model of electrons with broken time-reversal invariance moving in random potential. The replicon fluctuations around the zero-dimensional (0D), single metallic grain saddlepoint, are shown to destabilize diffusive regime beyond the low energy limit yielding a precise criteria of localization in terms of a single scaling parameter.