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

By using the pseudo-metric introduced in Golse and Paul (Arch Ration Mech Anal 223:57-94, 2017), 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 h. We obtain explicit uniform in h error estimates for the first-order Lie-Trotter, and the second-order Strang splitting methods.

Automated summary

The research demonstrates the uniform convergence of time splitting algorithms for the von Neumann equation of quantum dynamics in the Planck constant h, and provides explicit error estimates uniform in h for the first-order Lie-Trotter and second-order Strang splitting methods.