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.
Solutions faibles du problème de Cauchy pour certaines équations de Dirac non linéaires
Solvable nonlinear evolution PDEs in multidimensional space.
Sparse grids for the Schrödinger equation
We present a sparse grid/hyperbolic cross discretization for many-particle problems. It involves the tensor product of a one-particle multilevel basis. Subsequent truncation of the associated series expansion then results in a sparse grid discretization. Here, depending on the norms involved, different variants of sparse grid techniques for many-particle spaces can be derived that, in the best case, result in complexities and error estimates which are independent of the number of particles. Furthermore...
Spectral and scattering theory for symbolic potentials of order zero
Spectral Shift Function for the Perturbations of Schrödinger Operators at High Energy
2000 Mathematics Subject Classification: 35P20, 35J10, 35Q40.We give a complete pointwise asymptotic expansion for the Spectral Shift Function for Schrödinger operators that are perturbations of the Laplacian on Rn with slowly decaying potentials.
Spherical harmonics and maximal estimates for the Schrödinger equation.
Splitting of the Dirac operator in the nonrelativistic limit
Stability of matter for the Hartree-Fock functional of the relativistic electron-positron field.
Stability of the Brown-Ravenhall operator.
Stable blow up dynamics for the critical co-rotational Wave Maps and equivariant Yang-Mills Problems
This note summarizes the results obtained in [30]. We exhibit stable finite time blow up regimes for the energy critical co-rotational Wave Map with the target in all homotopy classes and for the equivariant critical Yang-Mills problem. We derive sharp asymptotics on the dynamics at blow up time and prove quantization of the energy focused at the singularity.