2017/01/31 by Antoine Tilloy · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Applied mathematics #Cold Atom Physics and Bose-Einstein Condensates #Computer science #Isotropy #Law #Markov process #Mathematics #Nonlinear system #Norm (philosophy) #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum dynamics #Quantum mechanics #Quantum process #Quantum stochastic calculus #Statistical physics #Stochastic process #quant-ph
paper · pdf · doi:10.22331/q-2017-09-19-29
published as Quantum 1, 29 (2017) · 7 pages
arxiv created 2017/09/18 · openalex publication_date 2017/09/19 · arxiv updated 2017/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Non-Markovian stochastic Schrödinger equations (NMSSE) are important tools in quantum mechanics, from the theory of open systems to foundations. Yet, in general, they are but formal objects: their solution can be computed numerically only in some specific cases or perturbatively. This article is focused on the NMSSE themselves rather than on the open-system evolution they unravel and aims at making them less abstract. Namely, we propose to write the stochastic realizations of linear NMSSE as averages over the solutions of an auxiliary equation with an additional random field. Our method yields a non-perturbative numerical simulation algorithm for generic linear NMSSE that can be made arbitrarily accurate for reasonably short times. For isotropic complex noises, the method extends from linear to non-linear NMSSE and allows to sample the solutions of norm-preserving NMSSE directly.