arXiv:2607.14689

A low-rank hierarchical framework for the non-Markovian stochastic Schrödinger equation with convergence analysis

Zhuohan Zhang, Zhenning Cai

Published Jul 16, 2026• 0 citations

Abstract

We propose and analyze a novel numerical framework for the non-Markovian stochastic Schrödinger equation (NMSSE) based on a low-rank approximation of the bath correlation functions. By decomposing the memory kernel into a finite-dimensional representation, we derive a truncated system of hierarchical equations that effectively balances computational tractability with physical fidelity. A rigorous convergence analysis is established for the hierarchical framework under mild assumptions. We demonstrate that our formulation serves as a mathematical generalization of the Hierarchy of Pure States (HOPS), encompassing it as a special case while offering a more flexible representation of non-Markovian effects. Numerical experiments across several benchmark models are presented to illustrate the validity and efficacy of the proposed method.

DOI: 10.48550/arxiv.2607.14689

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