Kinetic Energy Estimates for the Accuracy of the Time-Dependent Hartree-Fock Approximation with Coulomb Interaction

Volker Bach (1) , Sébastien Breteaux (1, 2) , Sören Petrat (3) , Peter Pickl (4) , Tim Tzaneteas (5)

1 IAA - Institut for Analysis and Algebra
2 BCAM - Basque Center for Applied Mathematics
3 IST Austria - Institute of Science and Technology [Klosterneuburg, Austria]
4 LMU - Ludwig Maximilian University [Munich] = Ludwig Maximilians Universität München
5 Mathematisches Institut [Tübingen]

We study the time evolution of a system of $N$ spinless fermions in $\mathbb{R}^3$ which interact through a pair potential, e.g., the Coulomb potential. We compare the dynamics given by the solution to Schrödinger's equation with the time-dependent Hartree-Fock approximation, and we give an estimate for the accuracy of this approximation in terms of the kinetic energy of the system. This leads, in turn, to bounds in terms of the initial total energy of the system.

Mots clés: mean-field; interacting fermions; quantum many-body theory; time-dependent Hartree-Fock

Domaines: Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]

Volker Bach, Sébastien Breteaux, Sören Petrat, Peter Pickl, Tim Tzaneteas. Kinetic Energy Estimates for the Accuracy of the Time-Dependent Hartree-Fock Approximation with Coulomb Interaction. Journal de Mathématiques Pures et Appliquées, 2016, 105 (1), pp.1-30. ⟨10.1016/j.matpur.2015.09.003⟩. ⟨hal-00956443v2⟩