Book Description

With the recent technical progress, single electron sources have moved fromtheory to the lab. Conceptually new types of experiments where one probesdirectly the internal quantum dynamics of the devices are within grasp. In thisthesis we develop the analytical and numerical tools for handling suchsituations. The simulations require appropriate spatial resolution for thesystems, and simulated times long enough so that one can probe their internalcharacteristic times. So far the standard theoretical approach used to treatsuch problems numerically--known as Keldysh or NEGF (Non Equilibrium Green'sFunctions) formalism--has not been very successful mainly because of aprohibitive computational cost. We propose a reformulation of the NEGFtechnique in terms of the electronic wave functions of the system in anenergy--time representation. The numerical algorithm we obtain scales nowlinearly with the simulated time and the volume of the system, and makessimulation of systems with 105-106 atoms/sites feasible. We leverage thistool to propose new intriguing effects and experiments. In particular weintroduce the concept of dynamical modification of interference pattern of aquantum system. For instance, we show that when raising a DC voltage V to anelectronic interferometer, the transient current responseoscillates as cos(eVt/ħ). We expect a wealth of new effects whennanoelectronic circuits are probed fast enough. The tools and conceptsdeveloped in this work shall play a key role in the analysis and proposal ofupcoming experiments.