S-matrix network models for coherent waves in random media: construction and renormalization

TL;DR

This paper introduces hierarchical S-matrix network models for coherent wave propagation in random media, enabling real space renormalization and analysis of localization-delocalization transitions.

Contribution

It presents a method to construct hierarchical S-matrix network models from elementary cells, facilitating the study of wave localization phenomena.

Findings

Hierarchical models capture localization-delocalization transitions.

Renormalization flow of conductance indicates phase behavior.

Numerical analysis supports qualitative understanding of wave transport.

Abstract

Networks of random quantum scatterers (S-matrices) form paradigmatic models for the propagation of coherent waves in random S-matrix network models cover universal localization-delocalization properties and have some advantages over more traditional Hamiltonian models. In particular, a straightforward implementation of real space renormalization techniques is possible. Starting from a finite elementary cell of the S-matrix network, hierarchical network models can be constructed by recursion. The localization-delocalization properties are contained in the flow of the forward scattering strength ('conductance') under increasing system size. With the aid of 'small scale' numerics qualitative aspects of the localization-delocalization properties of S-matrix network models can be worked out.