ImF-method and real-time approach to the dynamics of superconducting bridges and Josephson junctions at low temperature

Abstract: One of the standard approach for estimation of tunneling rates in quantum systems is so-called ImF-method. It is based on the evaluation of the imaginary part of free energy which originates after some analytic continuation procedure. However, in the experiments, one can’t measure macroscopic tunneling rates directly but only the observables which are sensitive to these processes. As an example, for Josephson junctions one can perform transport measurements and obtain induced voltage or switching current distribution. In order to make the bridge between theory and experiment it is necessary to solve kinetic master equation which is valid only in long-time limit. In result one can estimate transport coefficients only at low frequencies. In my talk, I will present another approach to these problems which is based on Keldysh technique combined with duality arguments. Considering short superconducting bridge as an example I will show the relation between two approaches and discuss how to evaluate voltage cumulants at finite frequencies. Also, I will discuss some general analytical properties of Green functions and their relation to the problem of evaluation of macroscopic tunneling rates.