Radiation conditions and scattering theory for -particle hamiltonians (main ideas of the approach)
Radiation conditions and scattering theory for -particle quantum systems
Rearrangement of lattice particles.
Rectangular potentials in a semi-harmonic background: spectrum, resonances and dwell time.
Reduced energy functionals for a three-dimensional fast rotating Bose Einstein condensates
Regularity properties of the generalized hamiltonian flow
Regularization of atomic Schrödinger operators with magnetic field.
Relaxation-time limits of global solutions in full quantum hydrodynamic model for semiconductors
This paper is concerned with the global well-posedness and relaxation-time limits for the solutions in the full quantum hydrodynamic model, which can be used to analyze the thermal and quantum influences on the transport of carriers in semiconductor devices. For the Cauchy problem in , we prove the global existence, uniqueness and exponential decay estimate of smooth solutions, when the initial data are small perturbations of an equilibrium state. Moreover, we show that the solutions converge into...
Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain
We concentrate on the analysis of the critical mass blowing-up solutions for the cubic focusing Schrödinger equation with Dirichlet boundary conditions, posed on a plane domain. We bound from below the blow-up rate for bounded and unbounded domains. If the blow-up occurs on the boundary, the blow-up rate is proved to grow faster than , the expected one. Moreover, we state that blow-up cannot occur on the boundary, under certain geometric conditions on the domain.
Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain
In this paper we concentrate on the analysis of the critical mass blowing-up solutions for the cubic focusing Schrödinger equation with Dirichlet boundary conditions, posed on a plane domain. We bound the blow-up rate from below, for bounded and unbounded domains. If the blow-up occurs on the boundary, the blow-up rate is proved to grow faster than , the expected one. Moreover, we show that blow-up cannot occur on the boundary, under certain geometric conditions on the domain.
Remarks on the Fundamental Solution to Schrödinger Equation with Variable Coefficients
We consider Schrödinger operators on with variable coefficients. Let be the free Schrödinger operator and we suppose is a “short-range” perturbation of . Then, under the nontrapping condition, we show that the time evolution operator: can be written as a product of the free evolution operator and a Fourier integral operator which is associated to the canonical relation given by the classical mechanical scattering. We also prove a similar result for the wave operators. These results...
Resolvent estimates for scalar fields with electromagnetic perturbation.
Resonance theory for periodic Schrödinger operators
Résonances par correspondance
Résonances semi-classiques pour l'opérateur de Schrödinger matriciel en dimension deux
Résultats de convergence et de non-convergence de l’équation de Von-Neumann périodique vers l’équation de Boltzmann quantique.
Résultats de finitude pour les lacunes spectrales