Berlin 2008 – wissenschaftliches Programm
Bereiche | Tage | Auswahl | Suche | Downloads | Hilfe
TT: Fachverband Tiefe Temperaturen
TT 32: Correlated Electrons: Poster Session
TT 32.45: Poster
Donnerstag, 28. Februar 2008, 14:00–18:00, Poster B
Time evolution in 2D quantum percolation — •Gerald Schubert and Holger Fehske — Ernst-Moritz-Arndt-Universität Greifswald, Germany
The quantum percolation problem of finding extended or localised wave functions on the spanning cluster shows a strong dependence on the dimension and connectivity of the underlying lattice. For cubic lattices in three dimensions (3D), the existence of a quantum percolation threshold, pq, only above which extended states exist, is well documented in the literature. Although the exact determination of the actual value of pq is difficult, the results agree on pc<pq<1, where pc is the classical percolation threshold. The situation is less clear for the 2D hypercubic lattice with estimates for pq ranging from 0.7 to 1. Here we investigate the time evolution of a wave packet initially localised on the spanning cluster by means of a Chebyshev expansion technique. Depending on the concentration of accessible lattice sites p, we find qualitatively different behaviour: The wave packet stays localised in a finite region for p<pq or spreads over the whole spanning for pq<p cluster. This gives evidence of pq<1. Of course our calculations have to be complemented by a careful finite-size analysis. Due to the high efficiency of the Chebyshev method, at present, we are able to increase the treatable system sizes up to 5000× 5000, which enables us to rule out some of previous estimates for pq.