75 citations · 177 across the 13 of their papers we have counts for
17 papers
Scattering for the positive density Hartree equation
Antoine Borie, Sonae Hadama, Julien Sabin
We study the asymptotic stability for large times of homogeneous stationary states for the nonlinear Hartree equation for density matrices in Rd for d\geq3. We can reach both the o…
Dynamics of mean-field Fermi systems with nonzero pairing
Stefano Marcantoni, Marcello Porta, Julien Sabin
We study the dynamics of many-body Fermi systems, for a class of initial data which are close to quasi-free states exhibiting a nonvanishing pairing matrix. We focus on the mean-fi…
Compactness methods in Lieb's work
Julien Sabin
We review some compactness methods appearing in the work of Lieb, with an emphasis on the techniques developed around his 1983 article on the optimizers for the Hardy-Littlewood-So…
The Dirac-Klein-Gordon system in the strong coupling limit
Jonas Lampart, Loïc Le Treust, Simona Rota Nodari +1
We study the Dirac equation coupled to scalar and vector Klein-Gordon fields in the limit of strong coupling and large masses of the fields. We prove convergence of the solutions t…
Sharp Weyl laws with singular potentials
Rupert L. Frank, Julien Sabin
We consider the Laplace--Beltrami operator on a three-dimensional Riemannian manifold perturbed by a potential from the Kato class and study whether various forms of Weyl's law rem…
The Hartree and Vlasov equations at positive density
Mathieu Lewin, Julien Sabin
We consider the nonlinear Hartree and Vlasov equations around a translation-invariant (homogeneous) stationary state in infinite volume, for a short range interaction potential. Fo…