How Long Does It Take for the Kondo Effect to Develop?

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 time-independent resonance at an effective temperature $T_{\mathrm{eff}}=T/\tanh (\pi Tt/2\mathrm{})$. Relevance of the buildup of the Kondo resonance to the transport current through a quantum dot is demonstrated.