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arXiv · 1906.03546

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

François Golse·Shi Jin·Thierry Paul
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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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François Golse, Shi Jin, Thierry Paul. 2019-06-09. On the Convergence of Time Splitting Methods for Quantum Dynamics in the Semiclassical Regime. https://arxiv.org/abs/1906.03546

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