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

• Published in: Annalen der Physik Vol. 7; no. 5-6; pp. 353 - 362
• Main Authors: Janssen, Martin, Merkt, Rainer, Weymer, Andreas
• Format: Journal Article
• Language: English
• Published: Leipzig WILEY-VCH Verlag 01.11.1998; WILEY‐VCH Verlag
• Subjects: Localization-delocalization transition; Multifractality; Renormalization group; S-matrix network models
• ISSN: 0003-3804; 1521-3889
• DOI: 10.1002/(SICI)1521-3889(199811)7:5/6<353::AID-ANDP353>3.0.CO;2-9

Networks of random quantum scatterers (S‐matrices) form paradigmatic models for the propagation of coherent waves in random media. 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.