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quant-ph2026
A General First- and Second-Order Numerical Solver for Non-Markovian Quantum State Diffusion
Zhenning Cai, Quanhui Zhu
The numerical simulation of non-Markovian open quantum systems based on the non-Markovian quantum state diffusion (NMQSD) equation is complicated by functional derivatives with res…
math.NA2026
A low-rank hierarchical framework for the non-Markovian stochastic Schrödinger equation with convergence analysis
Zhuohan Zhang, Zhenning Cai
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…
math.NA2026
Stability and Convergence of Mixed Finite Elements for Linear Regularized 13-Moment Equations
Shuang Hu, Huiteng Li, Zhenning Cai
We present a stable and convergent mixed finite element method (MFEM) for the linear regularized 13-moment (R13) equations in rarefied gas dynamics. Unlike existing methods that re…