Zhenning Cai, Associate Professor, Department of Mathematics, National University of Singapore

谢和虎 研究员

Solving Non-Markovian Stochastic Schrödinger Equation for Open Quantum Dynamics

6月8日（周一）10:00-11:00，南楼226

In open quantum systems, interaction with the surrounding environment typically drives the system into a mixed state, requiring a description via the reduced density matrix. Through stochastic unraveling, this reduced density matrix can be formulated as the expected value of stochastic quantum trajectories. Each trajectory is represented as a pure state wave function satisfying the non-Markovian stochastic Schrödinger equation (NMSSE). However, solving the NMSSE is numerically challenging because it contains a non-Markovian integral term involving a functional derivative, which suffers from intrinsic high-dimensionality.

The current state-of-the-art method to solve the NMSSE is the "Hierarchy of Pure States" (HOPS). HOPS requires decomposing the bath correlation function into a linear combination of exponential functions, making its computational efficiency strictly dependent on the number of terms. In this talk, we present a generalization of HOPS that works for general low-rank decompositions of the bath correlation function. Furthermore, we derive the explicit, exact solution of the NMSSE as an infinite series, providing a rigorous framework for numerical error analysis. Leveraging this series representation, we also introduce an iterative method to solve the NMSSE without requiring any decomposition of the bath correlation function. Finally, we demonstrate the efficacy of these methods using numerical simulations of the spin-boson model and discuss future extensions to particle simulations using the frozen Gaussian approximation.