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Functional Renormalization Group Methods for Quantum Transport Problems

Seminar by Prof. Herbert Schoeller, Institut für Theoretische Physik A, RWTH Aachen, Germany

Abstract
It is shown how functional renormalization group methods in imaginary time can be generalized to real times by formulating them on a Keldysh contour. In addition we show how problems of dissipative quantum mechanics can be treated where the local degrees of freedom can not be integrated out (operator vertices). To avoid singularities in the real-time flow and in order to preserve causality we propose to use a cutoff-parameter in the complex plane. The imaginary part of the cutoff corresponds to the Matsubara frequencies of the Fermi functions and the real part to the voltage. We apply the formalism to quantum transport through interacting quantum wires with impurities (Luttinger liquid) and to the nonequilibrium Kondo model. Within a general microscopic theory we describe the cutoff of the RG flow by voltage-induced energy broadening or relaxation/dephasing rates. Furthermore we find that the voltage can influence the power law exponents for the conductance through a quantum wire coupled to reservoirs induced by nonequilibrium occupation probabilities.