From closed to open one-dimensional Anderson model: Transport versus spectral statistics

S. Sorathia, F. M. Izrailev, V. G. Zelevinsky, G. L. Celardo
2012 Physical Review E  
Using the phenomenological expression for the level spacing distribution with only one parameter, 0 ≤β≤∞, covering all regimes of chaos and complexity in a quantum system, we show that transport properties of the one-dimensional Anderson model of finite size can be expressed in terms of this parameter. Specifically, we demonstrate a strictly linear relation between β and the normalized localization length for the whole transition from strongly localized to extended states. This result allows
more » ... to describe all transport properties in the open system entirely in terms of the parameter β and strength of coupling to continuum. For non-perfect coupling, our data show a quite unusual interplay between the degree of internal chaos defined by β, and degree of openness of the model. The results can be experimentally tested in single-mode waveguides with either bulk or surface disorder.
doi:10.1103/physreve.86.011142 pmid:23005403 fatcat:ifbrjknnovdopmukvzp7hfjznm