# Mathematical Models for Transport in Macroscopic and Mesoscopic Systems - Abstract

**Moldoveanu, Valeriu**

*Time-dependent transport in quantum dot systems: from transient regime to steady-state*

Consider a few-level noninteracting quantum dot described by a lattice Hamiltonian. At $t=0$ the system is coupled suddenly to biased leads. We compute the transient currents within the non-equilibrium Green-Keldysh formalism and discuss the charge dynamics inside many-level quantum dots. The Dyson equation for the two-times Green function is transformed into an algebraic equation which can be numerically implemented and solved by standard algorithms. We also investigate the passage to steady-state transport and identify traces of the many-level structure in this intermediate regime. When periodic signals are applied to the contacts the system operates as a turnstile pump. In this case we present a unified description of adiabatic and nonadiabatic pumping.