# How long does it take for the kondo effect to develop? Academic Article

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### 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 time-independent resonance at an effective temperature ${T}_{\mathrm{eff}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}T/\mathrm{tanh}(\ensuremath{\pi}Tt/2)$. Relevance of the buildup of the Kondo resonance to the transport current through a quantum dot is demonstrated.

### publication date

• January 1, 1999