9 citations · 9 across the 2 of their papers we have counts for
6 papers · 1 filter
Spectral properties of periodic systems cut at an angle
David Gontier
We consider a semi-periodic two-dimensional Schrödinger operator which is cut at an angle. When the cut is commensurate with the periodic lattice, the spectrum of the operator has…
The periodic Lieb-Thirring inequality
Rupert L. Frank, David Gontier, Mathieu Lewin
We discuss the Lieb-Thirring inequality for periodic systems, which has the same optimal constant as the original inequality for finite systems. This allows us to formulate a new c…
Edge states in ordinary differential equations for dislocations
David Gontier
In this article, we study Schrödinger operators on the real line, when the external potential represents a dislocation in a periodic medium. We study how the spectrum varies with t…
The reduced Hartree-Fock model with self-generated magnetic fields
David Gontier, Salma Lahbabi
We study the well-posedness of the reduced Hartree-Fock model for molecules and perfect crystals when taking into account a self-generated magnetic field. We exhibit a critical val…
Numerical construction of Wannier functions through homotopy
David Gontier, Antoine Levitt, Sami Siraj-Dine
We provide a mathematically proven, simple and efficient algorithm to build localised Wannier functions, with the only requirement that the system has vanishing Chern numbers. Our…
Spin symmetry breaking in the translation-invariant Hartree-Fock electron gas
David Gontier, Mathieu Lewin
We study the breaking of spin symmetry for the nonlinear Hartree-Fock model describing an infinite translation-invariant interacting quantum gas (fluid phase). At zero temperature…