Non-equilibrium frequency-dependent noise through mesoscopic circuits: a renormalization group approach

We analyze equilibrium and non-equilibrium frequency-dependent charge and spin current noise and conductance through a quantum dot in the local moment regime. To compute charge noise, we generalize the non-equilibrium renormalization group formalism of Rosch et al. [1]. First, we reformulate the problem within in a real time functional renormalization group formalism, and show that the original, rather heuristic derivation of Ref. [1] can be obtained easily and systematically in a real time formulation. We also show that the notorious problem of current conservation can be solved by deriving non-local equations for the current vertex [5]. We than solve the resulting integrodifferencial equations, and compute the non-equilibrium frequency-dependent noise. The noise exhibits strong anomalies (sharp dips) at frequencies ω = ±eV , which are clearly due to the non-equilibrium Kondo effect, and the build-up of correlations [5]. We also use a recent expression derived by Safi [2] to compute the non-equilibrium ac conductance, G(ω, V ). The conductance G(ω, V ) exhibits two peaks at ω = ±eV , which can clearly be associated with photon-assisted co-tunneling through the non-equilibrium Kondo resonances. Then we analize the spin current noise through the dot using a combination of density matrix numerical renormalization group (DM-NRG) [3] for the equilibrium situation, and a quantum master equation approach combined with perturbative renormalization group in the non-equilibrium case [4]. Spin current correlations are shown to behave markedly differently from charge correlations: Equilibrium spin cross-correlations are suppressed at frequencies below the Kondo scale, and are characterized by a universal function that