Observable Error Bounds of the Time-Splitting Scheme for Quantum-Classical Molecular Dynamics

Quantum-classical molecular dynamics, as a partial classical limit of the full quantum Schrödinger equation, is widely used framework for dynamics. The underlying equations are nonlinear in nature, containing part (representing electrons) and (standing nuclei). An accurate simulation wave function typically requires time step comparable to rescaled Planck constant , resulting formidable cost when . We prove an additive observable error bound Schwartz observables proposed time-splitting schemes based on semiclassical analysis, which decreases becomes smaller. Furthermore, we establish uniform-in- bound, allows accurately capture physical regardless size Numerical results verify our estimates.