Construction of vacuum for the positive-energy representation and its Bose counterpart.
Contractions of product density operators of systems of identical fermions and bosons.
Eigenvalue clusters of the Landau Hamiltonian in the exterior of a compact domain.
Electronic density at the nucleus. On a conjecture of Lieb
Embedded eigenvalues and resonances of Schrödinger operators with two channels
In this article, we give a necessary and sufficient condition in the perturbation regime on the existence of eigenvalues embedded between two thresholds. For an eigenvalue of the unperturbed operator embedded at a threshold, we prove that it can produce both discrete eigenvalues and resonances. The locations of the eigenvalues and resonances are given.
Entropy considerations in the noncommutative setting.
Erratum to “Non-trapping condition for semiclassical Schrödinger operators with matrix-valued potentials”.
Estimation des résidus de la matrice de diffusion associés à des résonances de forme I
Fermi Golden Rule, Feshbach Method and embedded point spectrum
A method to study the embedded point spectrum of self-adjoint operators is described. The method combines the Mourre theory and the Limiting Absorption Principle with the Feshbach Projection Method. A more complete description of this method is contained in a joint paper with V. Jakić, where it is applied to a study of embedded point spectrum of Pauli-Fierz Hamiltonians.
Filled band Fermi systems.
Form perturbations of the second quantized Dirac field.
Hamiltonians with zero-range interactions supported by a brownian path
High energy asymptotics for N-body scattering matrices with arbitrary channels
Holomorphy of the Dirac resolvent with relatively form bounded potentials
Improved estimate on the number of bound states of negatively charged bosonic atoms
Invariance of essential spectra for generalized Schrödinger operators.
Le papillon de Hofstadter
Local Exchange Potentials for Electronic Structure Calculations
The Hartree-Fock exchange operator is an integral operator arising in the Hartree-Fock model as well as in some instances of the density functional theory. In a number of applications, it is convenient to approximate this integral operator by a multiplication operator, i.e. by a local potential. This article presents a detailed analysis of the mathematical properties of various local approximations to the nonlocal Hartree-Fock exchange operator including the Slater potential, the optimized effective...
Lower bounds on wave packet propagation by packing dimensions of spectral measures.
Mathematical analysis of a generalized chiral quark soliton model.