We extend the derivation of the time-dependent Hartree-Fock equation recently obtained by Benedikter et al. ["Mean-field evolution of fermionic systems," Commun. Math. Phys. (to be published)] to fermions with a relativistic dispersion law. The main new ingredient is the propagation of semiclassical commutator bounds along the pseudo-relativistic Hartree-Fock evolution.
Mean-field dynamics of fermions with relativistic dispersion / N. Benedikter, M. Porta, B. Schlein. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - 55:2(2014), pp. 021901.1-021901.10.
Mean-field dynamics of fermions with relativistic dispersion
N. Benedikter;
2014
Abstract
We extend the derivation of the time-dependent Hartree-Fock equation recently obtained by Benedikter et al. ["Mean-field evolution of fermionic systems," Commun. Math. Phys. (to be published)] to fermions with a relativistic dispersion law. The main new ingredient is the propagation of semiclassical commutator bounds along the pseudo-relativistic Hartree-Fock evolution.
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