11 IV. SUMMARY AND CONCLUSIONS transport in non-interacting systems the GME method includes information on the energy structure of the sam- ple, but also on the geometrical properties reflected in the wave functions and sample-lead contacts. 7,8,25 Here we illustrate these aspects, in the interacting case, for two nanosystems: a two-dimensional quantum dot described by a lattice Hamiltonian and a short parabolic quantum wire. The time-dependent occupation of specific many- body states was thoroughly analyzed, for different values of the chemical potentials of the leads. It turned out that the excited states with N electrons contribute to the steady state currents if the ground state configuration with N + 1 particles is not available for transport. How- ever, if µ (0) N < µ$_{R}$ and at the same time µ (0) N +1 lies within the bias window the excited states with N particles are active only in the transient regime and become de- populated in the steady state regime. This behavior is of interest in the excited-state spectroscopy experiments. 11 To our knowledge the time-dependent currents associated to excited states have not been discussed theoretically so far. We calculated time-dependent currents in open meso- scopic systems composed by a sample attached to two semi-infinite leads, by solving the generalized master equation for the reduced density operator acting in the Fock space of the sample. This is the natural frame- work for including the Coulomb electron-electron inter- action in the sample, which is the main achievement of this work. The Coulomb interaction is treated in the spirit of the exact diagonalization method, i. e. in a pure many-body manner. The interacting many-body states of the sample are expanded in the basis of non-interacting “bit-string” states with unspecified number of electrons. We believe our method is a viable alternative to a recent approach based on a time-dependent density-functional model. 9,10,26 We used three sample models, a short 1D wire with 5 sites, but also a larger 2D lattice with 120 sites and a continuous model, whereas the cited group used much smaller samples even with no structure. 26 Indeed, due to computational limitations we could use only a restricted, effective number of many-body states in the GME, between 30-50 depending on the model, from the bottom of the energy spectrum. We chose the bias window [ µ$_{R}$, µ$_{L}$ ] and the strength of the sample-leads coupling parameters V$_{R,L}$ such that only the effective states contribute to the transport of electrons through the sample, whereas the states with higher energy are unreachable by the electrons. Consequently the number of electrons in the sample can be only up to 3 or 4. We could calculate the contribution to the charge and currents in the sample and in the leads respectively, cor- responding to any particular many-body state. We use the 1D chain as a toy model to emphasize the dominant role of the excited states in the transient regime and the onset of the Coulomb blockade in the steady state. A similar 1D model with 4 sites 1D has been considered recently by My¨ oh¨ anen et al. 10 As shown also in our previous works on time-dependent The authors acknowledge financial support from the Development Fund of the Reykjavik University Grant No. T09001, the Research and Instruments Funds of the Icelandic State, the Research Fund of the University of Iceland, the Icelandic Science and Technology Research Programme for Postgenomic Biomedicine, Nanoscience and Nanotechnology, the National Science Council of Tai- wan under contract No. NSC97-2112-M-239-003-MY3. V.M. also acknowledges the hospitality of the Reykjavik University, Science Institute and the partial financial sup- port from PNCDI2 program (grant No. 515/2009) and grant No. 45N/2009. Acknowledgments 1 G. Stefanucci, S. Kurth, A. Rubio and E. K. U. Gross, Phys. Rev. B 77, 075339 (2008). 2 V. Moldoveanu, A. Manolescu and V. Gudmundsson, Phys. Rev. B 76 , 085330 (2007) 3 X. Zheng, F. Wang, C. Y. Yam, Y. Mo, and G.H. Chen, Phys. Rev. B 75 , 195127 (2007). 4 V. Gudmundsson, G. Thorgilsson, C-S Tang, and V. Moldoveanu, Phys. Rev. B 77, 035329 (2008). 5 U. Harbola, M. Esposito, and S. Mukamel, Phys. Rev. B 74 , 235309 (2006). 6 S. Welack, M. Schreiber, and U. Kleinekath¨ ofer, J. Chem. Phys. 124, 044712 (2006) 7 V. Moldoveanu, A. Manolescu and V. Gudmundsson, New J. Phys. 11, 073019 (2009). 8 V. Gudmundsson, C. Gainar, C-S Tang, V. Moldoveanu, A. Manolescu, to appear in New J. Phys. 9 S. Kurth, G. Stefanucci, C.-O. Almbladh, A. Rubio, and E. K. U. Gross, Phys. Rev. B 72 , 035308 (2005). 10 P. My¨ oh¨ anen, A. Stan, G. Stefanucci, and R. van Leeuwen, Phys. Rev. B 80 , 115107 (2009), Europhys. Lett. 84 , 67001 (2008). 11 T. Fujisawa, D. G. Austing, Y. Tokura, Y. Hirayama, and S. Tarucha, J. Phys.: Condens. Matter 15 , R1395 (2003). 12 D. C. Langreth and P. Nordlander, Phys. Rev. B 43 , 2541 (1991) 13 S. A. Gurvitz and Ya. S. Prager, Phys. Rev. B 53 , 15932 (1996). 14 J. K¨ onig, H. Schoeller, and G. Sch¨ on, Phys. Rev. Lett. 76 , 1715 (1996); J. K¨ onig, J. Schmid, H. Schoeller, and G. Sch¨ on, Phys. Rev. B 54 , 16 820 (1996). 15 D. Becker and D. Pfannkuche, Physical Review B 77 205307 (2008). 16 S. Nakajima, Prog. Theor. Phys. 20 , 948 (1958). 17 R. Zwanzig, J. Chem. Phys. 33 , 1338 (1960).