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 nonequilibrium and current-voltage characteristics for different values of the dot charging energy.