The spectral cutting problem
The spectral properties of the Schrödinger operator in nonseparable Hilbert spaces
The spectrum band structure of the three-dimensional Schrödinger operator with periodic potential.
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...
The Spectrum of the Continuous Laplacian on a Graph.
The trace inequality and eigenvalue estimates for Schrödinger operators
Suppose is a nonnegative, locally integrable, radial function on , which is nonincreasing in . Set when and . Given and , we show there exists so that for all , if and only if exists with for all dyadic cubes Q, where . This result is used to refine recent estimates of C.L. Fefferman and D.H. Phong on the distribution of eigenvalues of Schrödinger operators.
Théorie de la diffusion pour l'équation de Schrödinger
Théorie de la diffusion pour l'équation de Schrödinger
Théorie de la diffusion quantique pour des perturbations à longue et courte portée du champ magnétique
Théorie des résonances pour des opérateurs de Schrödinger périodiques
Théorie spectrale de certains opérateurs de Schrödinger avec potentiel coulombien
Threshold scattering in two dimensions
Time Decay for Some Schrödinger Equations.
Time decay of finite energy solutions of the non linear Klein-Gordon and Schrödinger equations
Time Dependent Nonlinear Schrödinger Equations.
Time-decay of scattering solutions and classical trajectories
Time-dependent approach to radiation conditions
Time-dependent Scattering Theory.
Towards finite-gap integration of the Inozemtsev model.
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....