| We study the Kondo model at finite bias voltage using a nonequilibrium real-time renormalization group method. We present an analytic and well-controlled procedure to solve the RG equations in the weak-coupling regime. We discuss the longitudinal and transverse spin-spin correlation and response functions and the real-time evolution of spin and current. For the correlation functions we obtain analytic results for the line-shape, the small- and large-frequency limits and several other features like the height and width of the peak in the transverse susceptibility at the renormalized magnetic field. For the time evolution we find that all observables decay both with the spin relaxation and decoherence rates. Various voltage-dependent logarithmic, oscillatory, and power-law contributions are dervied. For short times we obtain universal dynamics for spin and current. In the second part we study non-equilibrium transport through a two-orbital Anderson model, which can be mapped to an effective Kondo model. Interestingly, the renormalized magnetic field has a linear voltage dependence in first order in the exchange coupling. We obtain analytic results for the differential conductance, which shows an asymmetry as a function of the bias voltage and can be used to detect the renormalization of the magnetic field. |
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