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We develop a stochastic Schr\"odinger equation (SSE) framework to simulatereal-time dynamics of Anderson-Holstein (AH) impurities coupled to a continuousfermionic bath. The bath degrees of freedom are incorporated throughfluctuating terms determined by exact system-bath correlations, which isderived in an ab initio manner. We show that such an SSE treatment provides amiddle ground between numerically expansive microscopic simulations andmacroscopic master equations. Computationally, the SSE model enables efficientnumerical methods for propagating stochastic trajectories. We demonstrate thatthis approach not only naturally provides microscopically-detailed informationunavailable from reduced models, but also captures effects beyond masterequations, thus serves as a promising tool to study open quantum dynamicsemerging in physics and chemistry.

Stochastic Schr\"odinger equation approach to real-time dynamics of Anderson-Holstein impurities: an open quantum system perspective