Dynamical approximations for composite quantum systems: Assessment of error estimates for a separable ansatz

Irene Burghardt (1) , Rémi Carles (2) , Clotilde Fermanian Kammerer (3) , Benjamin Lasorne (4) , Caroline Lasser (5)

1 Institute of Physical and Theoretical Chemistry [Frankfurt am Main]
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 LAMA - Laboratoire Analyse et de Mathématiques Appliquées
4 ICGM - Institut Charles Gerhardt Montpellier - Institut de Chimie Moléculaire et des Matériaux de Montpellier
5 Zentrum Mathematik, Technische Universität München

Numerical studies are presented to assess error estimates for a separable (Hartree) approximation for dynamically evolving composite quantum systems which exhibit distinct scales defined by their mass and frequency ratios. The relevant error estimates were formally described in our previous work [I. Burghardt, R. Carles, C. Fermanian Kammerer, B. Lasorne, C. Lasser, J. Phys. A. 54, 414002 (2021)]. Specifically, we consider a representative two-dimensional tunneling system where a double well and a harmonic coordinate are cubically coupled. The timedependent Hartree approximation is compared with a fully correlated solution, for different parameter regimes. The impact of the coupling and the resulting correlations are quantitatively assessed in terms of a time-dependent reaction probability along the tunneling coordinate. We show that the numerical error is correctly predicted on moderate time scales by a theoretically derived error estimate.

Domaines: Chimie théorique et/ou physique; Chimie-Physique [physics.chem-ph]; Physique mathématique [math-ph]

Irene Burghardt, Rémi Carles, Clotilde Fermanian Kammerer, Benjamin Lasorne, Caroline Lasser. Dynamical approximations for composite quantum systems: Assessment of error estimates for a separable ansatz. 2021. ⟨hal-03868449v1⟩