Classical and quantum spreading of a charge pulse

With the technical progress of radio-frequency setups, high frequency quantum transport experiments have moved from theory to the lab. So far the standard theoretical approach used to treat such problems numerically–known as Keldysh or NEGF (Non Equilibrium Green’s Functions) formalism–has not been very successful mainly because of a prohibitive computational cost. We propose a reformulation of the non-equilibrium Green’s function technique in terms of the electronic wave functions of the system in an energy-time representation. The numerical algorithm we obtain scales now linearly with the simulated time and the volume of the system, and makes simulation of systems with 10^5 - 10^6 atoms/sites feasible. We illustrate our method with the propagation and spreading of a charge pulse in the quantum Hall regime. We identify a classical and a quantum regime for the spreading, depending on the number of particles contained in the pulse. This numerical experiment is the condensed matter analogue to the spreading of a Gaussian wavepacket discussed in quantum mechanics textbooks.