The state coherence length as a metric of localization in a disordered solid

We define and study a new metric of eigenstate localization, the state coherence length Λ, for both continuous and discrete systems of arbitrary dimension. We demonstrate that it directly measures the spatial extent of individual states, and prove that in the configurational average in the localized regime it reproduces the well-known localization length ξ. Applying the state coherence length to a cubic lattice with Anderson disorder, we show that it can be used to find the critical disorder through a simple scaling argument. We use this approach to find the mobility edge, and our results agree with traditional finite-size scaling methods. Apart from its mean value, i.e. the localization length, we also obtain the full probability distribution of the state coherence length as a function of disorder.