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Using the time-dependent non-crossing approximation, we calculate thetransient response of the current through a quantum dot subject to a finitebias when the dot level is moved suddenly into a regime where the Kondo effectis present. After an initial small but rapid response, the time-dependentconductance is a universal function of the temperature, bias, and inverse time,all expressed in units of the Kondo temperature. Two timescales emerge: thefirst is the time to reach a quasi-metastable point where the Kondo resonanceis formed as a broad structure of half-width of the order of the bias; thesecond is the longer time required for the narrower split peak structure toemerge from the previous structure and to become fully formed. The first timecan be measured by the gross rise time of the conductance, which does notsubstantially change later while the split peaks are forming. The second timecharacterizes the decay rate of the small split Kondo peak (SKP) oscillationsin the conductance, which may provide a method of experimental access to it.This latter timescale is accessible via linear response from the steadystateand appears to be related to the scale identified in that manner [A.Rosch, J. Kroha, and P. Wolfle, Phys. Rev. Lett. 87, 156802 (2001)].Comment: Revtex with 15 eps figures. Compiles to 11 page

Transient currents and universal time scales for a fully time-dependent quantum dot in the Kondo regime