Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
1997-02-27
phys. stat. sol. (b) 211, 681 (1999)
Physics
Condensed Matter
Disordered Systems and Neural Networks
19 pages RevTeX preprint style, 11 PS figures; major revison, added numerical data on matrix elements
Scientific paper
We reinvestigate the validity of mapping the problem of two onsite interacting particles in a random potential onto an effective random matrix model. To this end we first study numerically how the non-interacting basis is coupled by the interaction. Our results indicate that the typical coupling matrix element decreases significantly faster with increasing single-particle localization length than is assumed in the random matrix model. We further show that even for models where the dependency of the coupling matrix element on the single-particle localization length is correctly described by the corresponding random matrix model its predictions for the localization length can be qualitatively incorrect. These results indicate that the mapping of an interacting random system onto an effective random matrix model is potentially dangerous. We also discuss how Imry's block-scaling picture for two interacting particles is influenced by the above arguments.
Roemer Rudolf A.
Schreiber Michael
Vojta Thomas
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