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International Journal of Modern Physics B

COUNTING STATISTICS OF NONEQUILIBRIUM TUNNELING PROCESS USING FUNCTIONAL RENORMALIZATION GROUP

Qing-Qiang Xu, Benling Gao, Shi‐Jie Xiong

Published Feb 20, 2010• 1 citation
Publisher

Abstract

We develop a scheme to investigate the flux of nonequilibrium transport based on the full counting statistics and nonequilibrium functional renormalization group method. As an illustrative example, we study the charge transfer in the system of an interacting quantum dot connected to two noninteracting reservoirs via tunneling. Within the lowest approximation in functional renormalization group, we obtain the cumulant generating function analytically.

DOI
10.1142/s0217979210054075

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The generating function for the cumulants of charge current distribution is calculated for two generalized Majorana resonant level models: the Kondo dot at the Toulouse point and the resonant level embedded in a Luttinger liquid with the interaction parameter g=1/2. We find that the low-temperature nonequilibrium transport in the Kondo case occurs via tunneling of physical electrons as well as by coherent transmission of electron pairs. We calculate the third cumulant ("skewness") explicitly and analyze it for different couplings, temperatures, and magnetic fields. For the g=1/2 setup the statistics simplifies and is given by a modified version of the Levitov-Lesovik formula.
We extend the concept of the functional renormalization for quantum many-body problems to nonequilibrium situations. Using a suitable generating functional based on the Keldysh approach, we derive a system of coupled differential equations for the mmm-particle vertex functions. The approach is completely general and allows calculations for both stationary and time-dependent situations. As a specific example we study the stationary state transport through a quantum dot with local Coulomb correlations at finite bias voltage employing two different truncation schemes for the infinite hierarchy of equations arising in the functional renormalization group scheme.
We review recent advances in the full counting statistics of a generic transport model of a quantum Brownian particle. The model applies to charge transfer through an impurity embedded in a Luttinger liquid environment, to a coherent one-channel conductor in a resistive environment, and to a resistively shunted Josephson junction device. We derive analytic expressions for the cumulant generating function (CGF) at two particular values of the Luttinger parameter which are related by self-duality. We determine the self-duality relations between the CGFs and between the cumulants.