Transient Currents Through Quantum Dots

Abstract

Kubo formula is used to get the time dependent current that flows through a quantum dot after switching on a small voltage bias. Technically, the calculation involves the evaluation of the linear response function for all frequencies and is, therefore, sensibly more expensive from the computational point of view than the evaluation of the d.c. conductance. Previous estimations of the transient current were done by Prigodin et al. in Phys. Rev. Lett. 72, 546 (1994) for chaotic mesoscopic systems. Our numerical results are completely different from the purely inductive results given in the mentioned paper. Both the regular and the chaotic system show initially a linear increase of the conductance that grows well beyond its static value. Afterwards, it decreases in an oscillating fashion towards its stationary value. While oscillations quickly attenuate in the chaotic model, a power law decay is obtained for the ideal system. Apart for the rapid oscillations, the result can be modelled by a classic circuit having resistive, inductive and also capacitive elements. In principle, our result opens a straightforward experimental way allowing a clear distinction between chaotic and regular systems.