RESUMO
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 fashion.
RESUMO
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 frequencies, we observe a suppression of disorder. This effect is caused by the wave number dependence of the disorder term in the wave equation, and has no analog in the case of electrons.
RESUMO
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 with the principles of chiral symmetry and QCD. To this end, the gauge fields are replaced with a stochastic white-noise potential, the gauge field disorder. Effective supersymmetric nonlinear sigma models are obtained. Spontaneous breaking of supersymmetry is found. We rigorously derive the equivalent of the Thouless energy within our generic model implying the universality of this scale in QCD. Connections to other low energy effective theories, in particular, the Nambu-Jona-Lasinio model and chiral perturbation theory, are found.
