Charge on the quantum dot in the presence of tunneling current
  The calculation of the charge present in central region of the double barrier structure at non-equilibrium conditions is discussed. We propose here a simple method to calculate non equilibrium Green's functions which allows consistent calculations of retarded and distribution functions. To illustrate the approach we calculate the charge on the quantum dot coupled {\it via} tunnel barriers to two external leads having different chemical potentials $\mu_L$ and $\mu_R$. The obtained results have been compared with other approaches existing in the literature. They all agree in the equilibrium situation and the departures grow with increasing the difference $\mu_L-\mu_R$. 
Mariusz Krawiec and Karol I. Wysokinski (Institute of Physics,   M.Curie-Sklodowska University)