Imaginary-time quantum many-body theory out of equilibrium II: Analytic continuation of dynamic observables and transport properties
Within the imaginary-time theory for nonequilibrium in quantum dot systems the calculation of dynamical quantities like Green's functions is possible via a suitable quantum Monte-Carlo algorithm. The challenging task is to analytically continue the imaginary-time data for both complex voltage and complex frequency onto the real variables. To this end a function-theoretical description of dynamical observables is introduced and discussed within the framework of the mathematical theory of several complex variables. We construct a feasible maximum-entropy algorithm for the analytical continuation by imposing a continuity assumption on the analytic structure and provide results for spectral functions in stationary non-equilibrium and current-voltage characteristics for different values of the dot charging energy.