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

Volker Bach (1) , Sébastien Breteaux (1) , Timmy Tzaneteas (2)

1 IAA - Institut for Analysis and Algebra
2 Mathematisches Institut [Tübingen]

We study the time evolution of a system of $N$ spinless fermions in $\mathbb{R}^3$ which interact through a repulsive 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: time-dependent Hartree-Fock; quantum many body problem; interacting fermions; mean field

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

Volker Bach, Sébastien Breteaux, Timmy Tzaneteas. Kinetic Energy Estimates for the Accuracy of the Time-Dependent Hartree-Fock Approximation with Coulomb Potential. 2014. ⟨hal-00956443v1⟩