30 citations · 55 across the 9 of their papers we have counts for
9 papers
Existence of Solutions for time-dependent fractional Kohn-Sham Equations
Sébastien Breteaux, Michele Fantechi, Jérémy Faupin
We consider time-dependent Kohn-Sham equations in dimension with a fractional dispersion relation , , and a class of interaction terms including, in p…
Propagation Estimates for the Boson Star Equation
Sébastien Breteaux, Jérémy Faupin, Viviana Grasselli
We consider the boson star equation with a general two-body interaction potential and initial data in a Sobolev space. Under general assumptions on , namely that d…
Exponential Decay outside of the Light Cone for the Pseudo-Relativistic Non-Autonomous Schrödinger Equation
Sébastien Breteaux, Jérémy Faupin, Viviana Grasselli
We establish a maximal velocity bound for a pseudo-relativistic quantum particle in an external time-dependent potential. Our estimate shows that the probability for the particle,…
Macroscopic suppression of supersonic quantum transport
Jérémy Faupin, Marius Lemm, Israel Michael Sigal +1
We consider a broad class of strongly interacting quantum lattice gases, including the Fermi-Hubbard and Bose-Hubbard models. We focus on macroscopic particle clusters of size …
Quantum Point Charges Interacting with Quasi-classical Electromagnetic Fields
S. Breteaux, M. Correggi, M. Falconi +1
We study effective models describing systems of quantum particles interacting with quantized (electromagnetic) fields in the quasi-classical regime, i.e., when the field's state sh…
On the number of bound states for fractional Schr{ö}dinger operators with critical and super-critical exponent
Sébastien Breteaux, Jérémy Faupin, Viviana Grasselli
We study the number of negative eigenvalues, counting multiplicities, of the fractional Schrödinger operator on , for any …
Regularity of Bound States
J. Faupin, J. S. Møller, E. Skibsted
We study regularity of bound states pertaining to embedded eigenvalues of a self-adjoint operator , with respect to an auxiliary operator that is conjugate to in the sen…
Second order perturbation theory for embedded eigenvalues
J. Faupin, J. S. Møller, E. Skibsted
We study second order perturbation theory for embedded eigenvalues of an abstract class of self-adjoint operators. Using an extension of the Mourre theory, under assumptions on the…
Local Decay in Non-relativistic QED
T. Chen, J. Faupin, J. Froehlich +1
We prove the limiting absorption principle for a dressed electron at a fixed total momentum in the standard model of non-relativistic quantum electrodynamics. Our proof is based on…