1 citations · 2 across the 7 of their papers we have counts for
9 papers
Approximate eigenfunctions for some aperiodic crystals
Long Meng
In this paper, we consider a broad class of continuum two-scale Hamiltonians \begin{align*} H_\varepsilon:=T(-i\nabla_x+\mathbf A(x,\varepsilon x))+V(x,\varepsilon x),\qquad x\in \…
Eigenvalue asymptotics of Müller minimizers for atoms and molecules
Rupert L. Frank, Long Meng, Phan Thành Nam +1
We study the spectral properties of minimizers of the Müller functional for atoms and molecules with electrons and total nuclear charge . We prove that under some suitable a…
Properties of periodic Dirac--Fock functional and minimizers
Isabelle Catto, Long Meng
Existence of minimizers for the Dirac--Fock model in crystals was recently proved by Paturel and Séré and the authors \cite{crystals} by a retraction technique due to Séré \cite{Se…
Strichartz estimates for the half wave/Klein-Gordon and Dirac Equations on compact manifolds without boundary
Federico Cacciafesta, Elena Danesi, Long Meng
In this paper we study Strichartz estimates for the half wave, the half Klein-Gordon and the Dirac Equations on compact manifolds without boundary, proving in particular for each o…
A rigorous justification of the Mittleman's approach to the Dirac--Fock model
Long Meng
In this paper, we study the relationship between the Dirac--Fock model and the electron-positron Hartree--Fock model. We justify the Dirac--Fock model as a variational approximatio…
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…
Strichartz estimates for the Dirac equation on asymptotically flat manifolds
Federico Cacciafesta, Anne-Sophie de Suzzoni, Long Meng
In this paper we prove Strichartz estimates for the Dirac equation on asymptotically flat manifolds. The proof combines the weak dispersive estimates proved by the first two author…
Large time well posedness for a Dirac--Klein-Gordon system
Federico Cacciafesta, Anne-Sophie de Suzzoni, Long Meng +1
In this paper we prove well posedness for a system coupling a nonlinear Dirac with a Klein-Gordon equation that represents a toy model for the Helium atom with relativistic correct…
Dirac Monopoles in Rogue Waves
L. -C. Zhao, L. -Z. Meng, Y. -H. Qin +2
We for the first time demonstrate that the widely existed nonlinear waves such as rogue waves, contain Dirac monopoles. We find that the density zeros of these nonlinear waves on a…