Two Interacting Particles in a Random Potential: Numerical Calculations of the Interaction Matrix Elements
We investigate 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 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. This leads to a much weaker enhancement than proposed earlier. We also discuss how Imry's block-scaling picture for two interacting particles is influenced by these data.
R. A. Romer et al., "Two Interacting Particles in a Random Potential: Numerical Calculations of the Interaction Matrix Elements," physica status solidi (b), vol. 211, no. 2, pp. 681-691, Wiley-VCH Verlag, Feb 1999.
The definitive version is available at https://doi.org/10.1002/(SICI)1521-3951(199902)211:2<681::AID-PSSB681>3.0.CO;2-I
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