Scattering, reflection and impedance of waves in chaotic and disordered systems with absorption

Abstract

We review recent progress in analysing wave scattering in systems with both\nintrinsic chaos and/or disorder and internal losses, when the scattering matrix\nis no longer unitary. By mapping the problem onto a nonlinear supersymmetric\nsigma-model, we are able to derive closed form analytic expressions for the\ndistribution of reflection probability in a generic disordered system. One of\nthe most important properties resulting from such an analysis is statistical\nindependence between the phase and the modulus of the reflection amplitude in\nevery perfectly open channel. The developed theory has far-reaching\nconsequences for many quantities of interest, including local Green functions\nand time delays. In particular, we point out the role played by absorption as a\nsensitive indicator of mechanisms behind the Anderson localisation transition.\nWe also provide a random-matrix-based analysis of S-matrix and impedance\ncorrelations for various symmetry classes as well as the distribution of\ntransmitted power for systems with broken time-reversal invariance, completing\nprevious works on the subject. The results can be applied, in particular, to\nthe experimentally accessible impedance and reflection in a microwave or\nultrasonic cavity attached to a system of antennas.\n