Time-Dependent Partition-Free Approach in Resonant Tunneling Systems

Details Time-Dependent Partition-Free Approach in Resonant Tunneling Systems Time-Dependent Partition-Free Approach in Resonant Tunneling Systems

2003-10-06

arxiv.org/abs/cond-mat/0310084v4

Phys. Rev. B 69, 195318 (2004)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

final version, 18 pages, 9 figures

Scientific paper

10.1103/PhysRevB.69.195318

An extended Keldysh formalism, well suited to properly take into account the initial correlations, is used in order to deal with the time-dependent current response of a resonant tunneling system. We use a \textit{partition-free} approach by Cini in which the whole system is in equilibrium before an external bias is switched on. No fictitious partitions are used. Besides the steady-state responses one can also calculate physical dynamical responses. In the noninteracting case we clarify under what circumstances a steady-state current develops and compare our result with the one obtained in the partitioned scheme. We prove a Theorem of asymptotic Equivalence between the two schemes for arbitrary time-dependent disturbances. We also show that the steady-state current is independent of the history of the external perturbation (Memory Loss Theorem). In the so called wide-band limit an analytic result for the time-dependent current is obtained. In the interacting case we propose an exact non-equilibrium Green function approach based on Time Dependent Density Functional Theory. The equations are no more difficult than an ordinary Mean Field treatment. We show how the scattering-state scheme by Lang follows from our formulation. An exact formula for the steady-state current of an arbitrary interacting resonant tunneling system is obtained. As an example the time-dependent current response is calculated in the Random Phase Approximation.

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