Wavepacket basis for time-dependent processes and its application to relaxation in resonant electronic transport

Abstract

Stroboscopic wavepacket basis sets [P. Bokes, F. Corsetti, R. W. Godby, Phys. Rev. Lett., 2008, 101, 046402] are specifically tailored for a description of time-dependent processes in extended systems, such as non-periodic geometries of various contacts consisting of solids and molecules. The explanation of the construction of such a basis for two simple finite systems is followed by a review of the general theory for extended systems with continuous spectrum. The latter is further elaborated with the introduction of the interaction representation which takes full advantage of the time-dynamics built into the basis. The formalism is applied to a semi-analytical example of electronic transport through resonant tunnelling barrier in 1D. Through the time-dependent generalisation of the Landauer formula given in terms of the Fourier expansion of the transmission amplitude we analyze the temporal character of the onset of the steady-state. Various time-scales in this process are shown to be directly related to the energetic structure of the resonant barrier.