# On the Convergence of Time Splitting Methods for Quantum Dynamics in the Semiclassical Regime

Abstract : By using the pseudo-metric introduced in [F. Golse, T. Paul: Archive for Rational Mech. Anal. 223 (2017) 57-94], which is an analogue of the Wasserstein distance of exponent 2 between a quantum density operator and a classical (phase-space) density, we prove that the convergence of time splitting algorithms for the von Neumann equation of quantum dynamics is uniform in the Planck constant $\hbar$. We obtain explicit uniform in $\hbar$ error estimates for the first order Lie-Trotter, and the second order Strang splitting methods.
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Cited literature [22 references]

https://hal-polytechnique.archives-ouvertes.fr/hal-02567952
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Submitted on : Friday, May 8, 2020 - 10:43:52 AM
Last modification on : Thursday, April 7, 2022 - 1:58:30 PM

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• HAL Id : hal-02567952, version 1

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François Golse, Shi Jin, Thierry Paul. On the Convergence of Time Splitting Methods for Quantum Dynamics in the Semiclassical Regime. Foundations of Computational Mathematics, Springer Verlag, In press, pp.DOI: 10.1007/s10208-020-09470-z. ⟨hal-02567952⟩

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