Scattering for a one-sided Klein-Gordon equation in quantum gravity
Scattering theory for 3-particle systems in constant magnetic fields : dispersive case
We develop a scattering theory for quantum systems of three charged particles in a constant magnetic field. For such systems, we generalize our earlier results in that we make no additional assumptions on the electric charges of subsystems. The main difficulty is the analysis of the scattering channels corresponding to the motion of the bound states of the neutral subsystems in the directions transversal to the field. The effective kinetic energy of this motion is given by certain dispersive Hamiltonians;...
Schrödinger equations in noncylindrical domains: exact controllability.
Schrödinger equations with unique positive isolated singularities.
Schrödinger operator with magnetic field in domain with corners
We present here a simplified version of results obtained with F. Alouges, M. Dauge, B. Helffer and G. Vial (cf [4, 7, 9]). We analyze the Schrödinger operator with magnetic field in an infinite sector. This study allows to determine accurate approximation of the low-lying eigenpairs of the Schrödinger operator in domains with corners. We complete this analysis with numerical experiments.
Schrödinger operators with form-bounded potentials in -spaces
s∗-compressibility of the discrete Hartree-Fock equation
The Hartree-Fock equation is widely accepted as the basic model of electronic structure calculation which serves as a canonical starting point for more sophisticated many-particle models. We have studied the s∗-compressibility for Galerkin discretizations of the Hartree-Fock equation in wavelet bases. Our focus is on the compression of Galerkin matrices from nuclear Coulomb potentials and nonlinear terms in the Fock operator which hitherto has not been discussed in the literature. It can be shown...
s∗-compressibility of the discrete Hartree-Fock equation
The Hartree-Fock equation is widely accepted as the basic model of electronic structure calculation which serves as a canonical starting point for more sophisticated many-particle models. We have studied the s∗-compressibility for Galerkin discretizations of the Hartree-Fock equation in wavelet bases. Our focus is on the compression of Galerkin matrices from nuclear Coulomb potentials and nonlinear terms in the Fock operator which hitherto has not been discussed in the literature. It can be shown...
Semiclassical and weak-magnetic-field eigenvalue asymptotics for the Schrödinger operator with electromagnetic potential
Semiclassical asymptotics for exchange energy
Semi-classical eigenstates at the bottom of a multidimensional well
Semiclassical expansion for the thermodynamic limit of the ground state energy of Kac's operator
We continue the study started by the first author of the semiclassical Kac Operator. This kind of operator has been obtained for example by M. Kac as he was studying a 2D spin lattice by the so-called “transfer operator method”. We are interested here in the thermodynamical limit of the ground state energy of this operator. For Kac’s spin model, is the free energy per spin, and the semiclassical regime corresponds to the mean-field approximation. Under suitable assumptions, which are satisfied...
Semi-classical Schrödinger equations with harmonic potential and nonlinear perturbation
Semiclassical, asymptotics and dispersive effects for Hartree-Fock systems
Short waves through thin interfaces and 2-microlocal measures
Singular integrals of the time-harmonic relativistic Dirac equation on a piecewise Liapunov surface.
Small global solutions and the nonrelativistic limit for the nonlinear Dirac equation.
In this paper we study the Cauchy problem for the nonlinear Dirac equation in the Sobolev space Hs. We prove the existence and uniqueness of global solutions for small data in Hs with s > 1...
Smoothing of dispersive waves
Solitary waves for Maxwell-Dirac and Coulomb-Dirac models
Solitary waves for Maxwell-Schrödinger equations.