Algebraic Weyl system and application
Almost localization and almost reducibility
Alternative method for determining the Feynman propagator of a non-relativistic quantum mechanical problem.
An adiabatic theorem for singularly perturbed hamiltonians
An application of semi-classical analysis to the asymptotic study of the supercooling field of a superconducting material
An error analysis of the multi-configuration time-dependent Hartree method of quantum dynamics
This paper gives an error analysis of the multi-configuration time-dependent Hartree (MCTDH) method for the approximation of multi-particle time-dependent Schrödinger equations. The MCTDH method approximates the multivariate wave function by a linear combination of products of univariate functions and replaces the high-dimensional linear Schrödinger equation by a coupled system of ordinary differential equations and low-dimensional nonlinear partial differential equations. The main result of this...
An exactly solvable spin chain related to Hahn polynomials.
An Exposition of the Connection between Limit-Periodic Potentials and Profinite Groups
We classify the hulls of different limit-periodic potentials and show that the hull of a limit-periodic potential is a procyclic group. We describe how limit-periodic potentials can be generated from a procyclic group and answer arising questions. As an expository paper, we discuss the connection between limit-periodic potentials and profinite groups as completely as possible and review some recent results on Schrödinger operators obtained in this...
An extension of a result by Dinaburg and Sinai on quasi-periodic potentials.
An inverse problem for the discrete periodic Schrödinger operator.
Analyse semi-classique de l'effet tunnel
Analyse semi-classique pour l'équation de Harper (avec application à l'équation de Schrödinger avec champ magnétique)
Analyse semi-classique pour l'équation de Harper. II: Comportement semi-classique près d'un rationnel
Analytic approach to systems in potential models.
Analytic solutions to nonlocal abstract equations
In this paper we study the problem of existence of global solutions for some classes of abstract equations, that generalize some type of Klein-Gordon equations, with nonlinear nonlocal terms of Kirchhoff type. We find some conditions that guarantee the existence of such solutions whether in presence or in absence of a conserved energy.
Anomalous quantum transport in presence of self-similar spectra
Anomalously slow cross symmetry phase relaxation, thermalized non-equilibrated matter and quantum computing beyond the quantum chaos border.
Applications of Lie systems in quantum mechanics and control theory
Some simple examples from quantum physics and control theory are used to illustrate the application of the theory of Lie systems. We will show, in particular, that for certain physical models both of the corresponding classical and quantum problems can be treated in a similar way, may be up to the replacement of the Lie group involved by a central extension of it. The geometric techniques developed for dealing with Lie systems are also used in problems of control theory. Specifically, we will study...
Approximation des valeurs propres de certaines perturbations singulières et application à l'opérateur de Dirac
Approximation semi-classique de l'équation de Heisenberg