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After we submitted our paper, we noticed a very recent theoretical work [G. Stefanucci and C.-O. Almbladh, cond-mat/0310084 (unpublished)] in which, by building up a formally exact NEGF+TDDFT (abbreviation for time dependent DFT) scheme, the authors show that the steady state current in the long-time limit depends only on the asymptotic shape of the one-particle effective potential of TDDFT. Our numerical result from the non-SC approach is just consistent with this theoretical finding.
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