Time-local unraveling of non-Markovian stochastic Schrödinger equations

Antoine Tilloy

Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany

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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.

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Cited by

[1] Antoine Tilloy and Howard M. Wiseman, "Non-Markovian wave-function collapse models are Bohmian-like theories in disguise", Quantum 5, 594 (2021).

[2] Bobin Li, "The decoherence effect of qubit in 1D transverse Ising model", Modern Physics Letters A 37 37n38, 2250241 (2022).

[3] Antoine Tilloy, "Does gravity have to be quantized? Lessons from non-relativistic toy models", Journal of Physics: Conference Series 1275 1, 012006 (2019).

[4] G. Gasbarri and L. Ferialdi, "Stochastic unravelings of non-Markovian completely positive and trace-preserving maps", Physical Review A 98 4, 042111 (2018).

[5] Brecht I. C. Donvil and Paolo Muratore-Ginanneschi, "On the Unraveling of Open Quantum Dynamics", Open Systems & Information Dynamics 30 03, 2350015 (2023).

[6] Antoine Tilloy, "Interacting quantum field theories as relativistic statistical field theories of local beables", arXiv:1702.06325, (2017).

[7] Giulio Gasbarri, Marko Toroš, and Angelo Bassi, "General Galilei Covariant Gaussian Maps", Physical Review Letters 119 10, 100403 (2017).

The above citations are from Crossref's cited-by service (last updated successfully 2024-04-15 08:07:46) and SAO/NASA ADS (last updated successfully 2024-04-15 08:07:47). The list may be incomplete as not all publishers provide suitable and complete citation data.

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