65 citations · 119 across the 8 of their papers we have counts for
12 papers
Asymptotics for eigenvalues of one-dimensional Dirac operators in the weak coupling limit
Danko Aldunate, Juan Manuel González-Brantes, Hanne Van Den Bosch
In this paper, we derive new results on the asymptotic behavior of eigenvalues of perturbed one-dimensional massive Dirac operators in the weak coupling limit. Two classes of poten…
Edge states for tight-binding operators with soft walls
Camilo Gómez Araya, David Gontier, Hanne Van Den Bosch
We study one- and two-dimensional periodic tight-binding models under the presence of a potential that grows to infinity in one direction, hence preventing the particles to escape…
Spectrum of the linearized Vlasov--Poisson equation around steady states from galactic dynamics
Matias Moreno, Paola Rioseco, Hanne Van Den Bosch
We study the linearized Vlasov-Poisson equation in the gravitational case around steady states that are decreasing and continuous functions of the energy. We identify the absolutel…
Keller and Lieb-Thirring estimates of the eigenvalues in the gap of Dirac operators
Jean Dolbeault, David Gontier, Fabio Pizzichillo +1
We estimate the lowest eigenvalue in the gap of the essential spectrum of a Dirac operator with mass in terms of a Lebesgue norm of the potential. Such a bound is the counterpart f…
Mixing in an anharmonic potential well
Matías Moreno, Paola Rioseco, Hanne Van Den Bosch
We prove phase-space mixing for solutions to Liouville's equation for integrable systems. Under a natural non-harmonicity condition, we obtain weak convergence of the distribution…
Results on the spectral stability of standing wave solutions of the Soler model in 1-D
Danko Aldunate, Julien Ricaud, Edgardo Stockmeyer +1
We study the spectral stability of the nonlinear Dirac operator in dimension , restricting our attention to nonlinearities of the form …
Self-adjointness of two-dimensional Dirac operators on domains
Rafael D. Benguria, Søren Fournais, Edgardo Stockmeyer +1
We consider Dirac operators defined on planar domains. For a large class of boundary conditions, we give a direct proof of their self-adjointness in the Sobolev space .
The maximal excess charge in Müller density-matrix-functional theory
Rupert L. Frank, Phan Thành Nam, Hanne Van Den Bosch
We consider an atom described by Müller theory, which is similar to Hartree-Fock theory, but with a modified exchange term. We prove that a nucleus of charge Z can bind at most Z+C…
The ionization conjecture in Thomas-Fermi-Dirac-von Weizsäcker theory
Rupert L. Frank, Phan Thành Nam, Hanne Van Den Bosch
We prove that in Thomas-Fermi-Dirac-von Weizsäcker theory, a nucleus of charge can bind at most electrons, where is a universal constant. This result is obtained th…
Nonexistence in Thomas-Fermi-Dirac-von Weizsäcker theory with small nuclear charges
Phan Thành Nam, Hanne Van Den Bosch
We study the ionization problem in the Thomas-Fermi-Dirac-von Weizsäcker theory for atoms and molecules. We prove the nonexistence of minimizers for the energy functional when the…
Spectral gaps of Dirac operators describing graphene quantum dots
Rafael D. Benguria, Søren Fournais, Edgardo Stockmeyer +1
The two-dimensional Dirac operator describes low-energy excitations in graphene. Different choices for the boundary conditions give rise to qualitative differences in the spectrum…
Intermediate model between Majority voter PCA and its Mean Field model
Jean Bricmont, Hanne Van Den Bosch
Probabilistic Cellular Automata (PCA) are simple models used to study dynamical phase transitions. There exist mean field approximations to PCA that can be shown to exhibit a phase…