The 2D Schrödinger equation for a neutral pair in a constant magnetic field
The energy of heavy atoms according to Brown and Ravenhall: the Scott correction.
The spectrum of Schrödinger operators with random magnetic fields
We shall consider the Schrödinger operators on with the magnetic field given by a nonnegative constant field plus random magnetic fields of the Anderson type or of the Poisson-Anderson type. We shall investigate the spectrum of these operators by the method of the admissible potentials by Kirsch-Martinelli. Moreover, we shall prove the lower Landau levels are infinitely degenerated eigenvalues when the constant field is sufficiently large, by estimating the growth order of the eigenfunctions...
Théorie de la diffusion pour le modèle en théorie des champs
Théorie de la diffusion pour un atome couplé à un champ quantique
Transfer matrices and transport for Schrödinger operators
We provide a general lower bound on the dynamics of one dimensional Schrödinger operators in terms of transfer matrices. In particular it yields a non trivial lower bound on the transport exponents as soon as the norm of transfer matrices does not grow faster than polynomially on a set of energies of full Lebesgue measure, and regardless of the nature of the spectrum. Applications to Hamiltonians with a) sparse, b) quasi-periodic, c) random decaying potential are provided....