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Scaling in Interaction-Assisted Coherent Transport

The pair localization length $L_2$ of two interacting electrons in one--dimensional disordered systems is studied numerically. Using two direct approaches, we find $L_2 \propto L_1^α$, where $L_1$ is the one-electron localization length and $α\approx 1.65$. This demonstrates the enhancement effect proposed by Shepelyansky, but the value of $α$ differs from previous estimates ($α=2$) in the disorder range considered. We explain this discrepancy using a scaling picture recently introduced by Imry and taking into account a more accurate distribution than previously assumed for the overlap of one-electron wavefunctions.