5 citations · 9 across the 5 of their papers we have counts for
5 papers
Existence of minimizers for the Dirac-Fock model of crystals
Isabelle Catto, Long Meng, Eric Paturel +1
Whereas many different models exist in the mathematical and physics literature for ground states of non-relativistic crystals, the relativistic case has been much less studied and…
A new definition of the Dirac-Fock ground state
Eric Séré
The Dirac-Fock (DF) model replaces the Hartree-Fock (HF) approximation in quantum chemistry when relativistic effects cannot be neglected. Since the Dirac operator is not bounded f…
Phase transition in the Peierls model for polyacetylene
David Gontier, Adéchola Kouande, Eric Séré
We consider the Peierls model for closed polyactetylene chains with an even number of carbon atoms as well as infinite chains, in the presence of temperature. We prove the existenc…
Distinguished self-adjoint extension and eigenvalues of operators with gaps. Application to Dirac-Coulomb operators
Jean Dolbeault, Maria J. Esteban, Eric Séré
We consider a linear symmetric operator in a Hilbert space that is neither bounded from above nor from below, admits a block decomposition corresponding to an orthogonal splitting…
Which nuclear shape generates the strongest attraction on a relativistic electron? An open problem in relativistic quantum mechanics
Maria J. Esteban, Mathieu Lewin, Eric Séré
In this article we formulate several conjectures concerning the lowest eigenvalue of a Dirac operator with an external electrostatic potential. The latter describes a relativistic…