Non-equilibrium Green’s Functions for Coupled Fermion-Boson Systems

Daniel Karlsson, Robert van Leeuwen

C. B. Dover

Nikhil Danny Babu, Girish S. Setlur

Non-chiral bosonization technique adapted to study chiral quantum wires with non-interacting fermions coupled through a point-contact with a constant bias between the wires is introduced and is shown to reproduce the exact Green functions of this system which was previously derived by the present authors analytically using standard methods. The tunneling I-V characteristics are obtained using the bosonized Green functions. The proposed unconventional bosonization scheme is also shown to be internally consistent as the four-point functions evaluated using NCBT are shown to be related to the two-point functions through Wick's theorem as it should be. In equilibrium, the equal space-time NCBT Green functions for an interacting Luttinger liquid with impurities obtained in a previous work shows universal scaling behaviour in accordance with Bethe ansatz and functional renormalization group predictions. We expect to obtain a similar scaling form of the tunneling properties out of equilibrium in presence of interparticle interactions.

Katha Ganguly, Bijay Kumar Agarwalla

We provide a systematic approach to compute different kinds of non-equilibrium Green's functions for open quantum systems which are essentially two-point correlation functions in time. We reveal that the definition of Green's functions based on the Born approximation does not provide the correct results in the leading order of the system-bath coupling. We next provide a systematic correction term in Green's functions by going beyond the Born approximation and incorporating a finite correlation between the system and the bath. We primarily focus on two paradigmatic models of open quantum systems, namely, the dissipative Caldeira-Leggett model and the dissipative spin-boson model. We show that the inclusion of such a correction correctly reproduces the Kadanoff-Baym type equation for the so-called lesser or greater components of the Green's functions and provides the correct long-time result up to the first non-zero order of the system-bath coupling, satisfying the detailed balance condition in thermal equilibrium. We further extend our study to a system coupled to multiple reservoirs simultaneously that are maintained at different temperatures and obtain expressions for non-equilibrium steady-state energy current, once again correct up to the first non-zero order of the system-bath coupling.

Donald H. Kobe, Warren B. Cheston