Limite semi-classique de l'amplitude de diffusion
Limiting absorption principle for the Dirac operator
Linear stability theory of solitary waves arising from Hamiltonian systems with symmetry
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...
Localisation for the spin J-boson hamiltonian
Localisation pour des opérateurs de Schrödinger aléatoires dans : un modèle semi-classique
Dans , nous démontrons un résultat de localisation exponentielle pour un opérateur de Schrödinger semi-classique à potentiel périodique perturbé par de petites perturbations aléatoires indépendantes identiquement distribuées placées au fond de chaque puits. Pour ce faire, on montre que notre opérateur, restreint à un intervalle d’énergie convenable, est unitairement équivalent à une matrice aléatoire infinie dont on contrôle bien les coefficients. Puis, pour ce type de matrices, on prouve un résultat...
Localization of the essential spectrum for relativistic -electron ions and atoms.
Lower bounds for the infimum of the spectrum of the Schrödinger operator in and the Sobolev inequalities.
Lower bounds on wave packet propagation by packing dimensions of spectral measures.
Lower bounds to Feynman integrals and class
Low-rank tensor representation of Slater-type and Hydrogen-like orbitals
The paper focuses on a low-rank tensor structured representation of Slater-type and Hydrogen-like orbital basis functions that can be used in electronic structure calculations. Standard packages use the Gaussian-type basis functions which allow us to analytically evaluate the necessary integrals. Slater-type and Hydrogen-like orbital functions are physically more appropriate, but they are not analytically integrable. A numerical integration is too expensive when using the standard discretization...
Lyapunov control of a quantum particle in a decaying potential
Magnetic barriers of compact support and eigenvalues in spectral gaps.
Magnetic Schrödinger Operator: Geometry, Classical and Quantum Dynamics and Spectral Asymptotics
I study the Schrödinger operator with the strong magnetic field, considering links between geometry of magnetic field, classical and quantum dynamics associated with operator and spectral asymptotics. In particular, I will discuss the role of short periodic trajectories.
Mathematical analysis of a generalized chiral quark soliton model.
Mathematical modeling of semiconductor quantum dots based on the nonparabolic effective-mass approximation
Within the effective mass and nonparabolic band theory, a general framework of mathematical models and numerical methods is developed for theoretical studies of semiconductor quantum dots. It includes single-electron models and many-electron models of Hartree-Fock, configuration interaction, and current-spin density functional theory approaches. These models result in nonlinear eigenvalue problems from a suitable discretization. Cubic and quintic Jacobi-Davidson methods of block or nonblock version...
Matrix elements for sum of power-law potentials in quantum mechanic using generalized hypergeometric functions.
Maximal Monotonicity of Operators with Sufficiently Large Domain and Application to the Hartree Problem.
Maximum entropy wave functions.
Mean-Field Limit of Quantum Bose Gases and Nonlinear Hartree Equation
We discuss the Hartree equation arising in the mean-field limit of large systems of bosons and explain its importance within the class of nonlinear Schrödinger equations. Of special interest to us is the Hartree equation with focusing nonlinearity (attractive two-body interactions). Rigorous results for the Hartree equation are presented concerning: 1) its derivation from the quantum theory of large systems of bosons, 2) existence and stability of Hartree solitons, and 3) its point-particle (Newtonian)...