On the Convergence of Time Splitting Methods for Quantum Dynamics in the Semiclassical Regime - Archive ouverte HAL Access content directly
Journal Articles Foundations of Computational Mathematics Year : 2020

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

François Golse
• Function : Author
• PersonId : 964158
Shi Jin
• Function : Author
• PersonId : 1060698
Thierry Paul
• Function : Author
• PersonId : 1069358

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.

Dates and versions

hal-02567952 , version 1 (08-05-2020)

Identifiers

• HAL Id : hal-02567952 , version 1

Cite

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

100 View