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

TL;DR

This paper introduces a stochastic Schr"odinger equation framework for simulating the real-time dynamics of Anderson-Holstein impurities coupled to a fermionic bath, bridging microscopic detail and computational efficiency.

Contribution

It develops an ab initio derived SSE method that captures effects beyond traditional master equations for open quantum systems.

Findings

Provides a computationally efficient SSE approach.

Captures dynamics beyond standard master equations.

Offers detailed microscopic insights into open quantum systems.

Abstract

We develop a stochastic Schr\"odinger equation (SSE) framework to simulate 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 serves as a promising tool to study open quantum dynamics emerging in physics and chemistry.