Numerical Estimation of Keldysh-Countour Path Integrals for Nonequilibrium Problems

We propose an idea for simulating the dynamics of open (coupled to reservoirs) systems in a nonequilibrium steady state and present preliminary numerical results for the nonequilibrium spin boson and Anderson models. The method builds on the observation (Phys. Rev. Lett. ${\bf 94}$ 076404) that out of equilibrium the Keldysh time evolution operator exhibits an exponential time decay, and uses the stochastic hybridization expansion techniques of Phys. Rev. Lett. ${\bf 97}$, 07640.