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The density-matrix renormalization-group (DMRG) algorithm is extended totreat time-dependent problems. The method provides a systematic and robust toolto explore out-of-equilibrium phenomena in quantum many-body systems. Weillustrate the method by showing that attractive interactions enhance thetunneling current between two Luttinger liquids, whereas repulsive interactionssuppress it, in qualitative agreement with analytical predictions. Enhancementof the transport current through a quantum dot in the Kondo regime is alsoexhibited.Comment: 4 pages, 3 figures. Additional results, added clarifications, updated  reference

Time-Dependent Density-Matrix Renormalization Group: A Systematic Method for the Study of Quantum Many-Body Out-of-Equilibrium Systems