How long does it take for the Kondo effect to develop?

Abstract

The time-development of the Kondo effect is theoretically investigated by studying a quantum dot suddenly shifted into the Kondo regime by a change of voltage on a nearby gate. Using time-dependent versions of both the Anderson and Kondo Hamiltonians, it is shown that after a time $t$ following the voltage shift, the form of the Kondo resonance matches the {\it time-independent} resonance at an effective temperature $T_{eff} = T/\tanh(\pi T t/2)$. Relevance of the buildup of the Kondo resonance to the transport current through a quantum dot is demonstrated.