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

2019/06/09 by Golse, François, Jin, Shi, Paul, Thierry · 2 citations
#65M15 #81Q20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1906.03546

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 ℏ. We obtain explicit uniform in ℏ error estimates for the first order Lie-Trotter, and the second order Strang splitting methods.

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• Frozen Gaussian sampling algorithms for simulating Markovian open quantum systems in the semiclassical regime
• Uniform semiclassical observable error bound of Trotterization without the Egorov theorem: a simple algebraic proof

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