Statistical Wave Scattering in Chaotic and Disordered Systems: Random Matrices and Maximum Entropy

We present a statistical theory of complex wave-interference phenomena, applicable to systems where the complexity in wave scattering may derive from the chaotic nature of the underlying classical dynamics, as in microwave cavities and quantum dots, or from the quenched randomness of scattering potentials, as in disordered conductors. The resulting interference pattern is so complex that only a statistical treatment is meaningful. We follow a maximum-entropy approach, in which Shannon's information entropy is maximized, subject to the symmetries and constraints that are physically relevant. This is done in the framework of the powerful, non-perturbative, approach known as random-matrix theory.