We study numerically the fluctuation properties of the eigenvalues of the scalar wave equation in two dimensions for strong disorder. This equation mimicks properties of light in dielectrics. With increasing disorder, we find a transition from diffusive to localized behavior, in complete analogy to the case of Schrodinger waves (electrons). At low… (More)

We prove ergodicity of unitary random-matrix theories by showing that the autocorrelation function with respect to energy or magnetic field strength of any observable vanishes asymptotically. We do so using Efetov's supersymmetry method, a polar decomposition of the saddle-point manifold, and an asymptotic evaluation of the boundary terms generated in this… (More)

Recent theoretical and numerical developments show analogies between quantum chromodynamics (QCD) and disordered systems in condensed matter physics. We study the spectral fluctuations of a Dirac particle propagating in a finite four-dimensional box in the presence of gauge fields. We construct a model which combines Efetov's approach to disordered systems… (More)