in the Coulomb gauge
A generalization of the radiation condition of Sommerfeld for -body Schrödinger operators
A generalized coherent state approach of the quantum dynamics for suitable time-dependent hamiltonians
A Lieb-Thirring bound for a magnetic Pauli Hamiltonian (II).
We establish a Lieb-Thirring type estimate for Pauli Hamiltonians with non-homogeneous magnetic fields. Besides of depending on the size of the field, the bound also takes into account the size of the field gradient. We then apply the inequality to prove stability of non-relativistic quantum mechanical matter coupled to the quantized ultraviolet-cutoff electromagnetic field for arbitrary values of the fine structure constant.
A Maxwell-Bloch model with discrete symmetries for wave propagation in nonlinear crystals : an application to KDP
This article presents the derivation of a semi-classical model of electromagnetic-wave propagation in a non centro-symmetric crystal. It consists of Maxwell’s equations for the wave field coupled with a version of Bloch’s equations which takes fully into account the discrete symmetry group of the crystal. The model is specialized in the case of a KDP crystal for which information about the dipolar moments at the Bloch level can be recovered from the macroscopic dispersion properties of the material....
A Maxwell-Bloch model with discrete symmetries for wave propagation in nonlinear crystals: an application to KDP
This article presents the derivation of a semi-classical model of electromagnetic-wave propagation in a non centro-symmetric crystal. It consists of Maxwell's equations for the wave field coupled with a version of Bloch's equations which takes fully into account the discrete symmetry group of the crystal. The model is specialized in the case of a KDP crystal for which information about the dipolar moments at the Bloch level can be recovered from the macroscopic dispersion properties of the material. ...
A model of atomic radiation
A multiplicity result for the Schrodinger-Maxwell equations with negative potential
We prove the existence of a sequence of radial solutions with negative energy of the Schrödinger-Maxwell equations under the action of a negative potential.
A non-local theory of superfluidity
We will formulate a macroscopic theory of Superfluidity, using a particular constitutive equation of differential form which we will demonstrate to be equivalent to a non-local relation between the stress and the density.
A numerical perspective on Hartree−Fock−Bogoliubov theory
The method of choice for describing attractive quantum systems is Hartree−Fock−Bogoliubov (HFB) theory. This is a nonlinear model which allows for the description of pairing effects, the main explanation for the superconductivity of certain materials at very low temperature. This paper is the first study of Hartree−Fock−Bogoliubov theory from the point of view of numerical analysis. We start by discussing its proper discretization and then analyze the convergence of the simple fixed point (Roothaan)...
A problem related to the Hall effect in a semiconductor with an electrode of an arbitrary shape.
A self-consistent numerical method for simulation of quantum transport in high electron mobility transistor. I: The Boltzmann-Poisson-Schrödinger solver.
A self-consistent numerical method for simulation of quantum transport in high electron mobility transistor. II: The full quantum transport.
A single scale infinite volume expansion for three dimensional many Fermion Green's functions.
A singular lagrangian model for N-body relativistic interactions
A Two-Particle Quantum System with Zero-Range Interaction
We study a two-particle quantum system given by a test particle interacting in three dimensions with a harmonic oscillator through a zero-range potential. We give a rigorous meaning to the Schrödinger operator associated with the system by applying the theory of quadratic forms and defining suitable families of self-adjoint operators. Finally we fully characterize the spectral properties of such operators.
A unified model of phantom energy and dark matter.
About poles of the resolvent, in a model for a harmonic oscillator coupled with massless scalar bosons
About the adiabatic stability of resonant states
Absence of geometrical phases in the rotating stark effect