Stochastic Schrödinger Equation Approach to Real-Time Dynamics of Anderson–Holstein Impurities: An Open Quantum System Perspective

Abstract

We develop a stochastic Schrödinger equation (SSE) framework to simulate the real-time dynamics of Anderson–Holstein (AH) impurities coupled to a continuous Fermionic bath. The bath degrees of freedom are incorporated through fluctuating terms determined by exact system-bath correlations, which is derived in an ab initio manner. We show that such an SSE treatment provides a middle ground between numerically expansive microscopic simulations and macroscopic master equations. Computationally, the SSE model enables efficient numerical methods for propagating stochastic trajectories. We demonstrate that this approach not only naturally provides microscopically detailed information unavailable from reduced models but also captures effects beyond master equations, thus serving as a promising tool to study open quantum dynamics emerging in physics and chemistry.