Back-scattering and nonlinear Radon transformation
Bethe ansatz solutions to quasi exactly solvable difference equations.
Bifurcation for some semilinear elliptic equations when the linearization has no eigenvalues
We prove existence and bifurcation results for a semilinear eigenvalue problem in , where the linearization — has no eigenvalues. In particular, we show...
Boltzmann distributed quantum steady states and their classical limit.
Boundary stabilization of a coupled system of nondissipative Schrödinger equations.
Bounds on the excess charge and the ionization energy for the Hellmann-Weizsacker model
Bouteilles magnétiques et supraconductivité
Canonical commutation relations and interacting Fock spaces
We introduce by means of reproducing kernel theory and decomposition in orthogonal polynomials canonical correspondences between an interacting Fock space a reproducing kernel Hilbert space and a square integrable functions space w.r.t. a cylindrical measure. Using this correspondences we investigate the structure of the infinite dimensional canonical commutation relations. In particular we construct test functions spaces, distributions spaces and a quantization map which generalized the work of...
Classical limit of the matrix elements on quantized Lobachevskii plane.
Comparaison entre la décroissance de fonctions propres pour les opérateurs de Dirac et de Klein-Gordon. Application à l'étude de l'effet tunnel
Complétude asymptotique des systèmes à corps à courte portée
Complétude asymptotique pour un modèle du transfert de charge
Complex absorbing potential method for systems [Book]
Confining quantum particles with a purely magnetic field
We consider a Schrödinger operator with a magnetic field (and no electric field) on a domain in the Euclidean space with a compact boundary. We give sufficient conditions on the behaviour of the magnetic field near the boundary which guarantees essential self-adjointness of this operator. From the physical point of view, it means that the quantum particle is confined in the domain by the magnetic field. We construct examples in the case where the boundary is smooth as well as for polytopes; These...
Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula
Starting from the Rodrigues representation of polynomial solutions of the general hypergeometric-type differential equation complementary polynomials are constructed using a natural method. Among the key results is a generating function in closed form leading to short and transparent derivations of recursion relations and addition theorem. The complementary polynomials satisfy a hypergeometric-type differential equation themselves, have a three-term recursion among others and obey Rodrigues formulas....
Construction BKW pour l'opérateur de Dirac. Cas d'un potentiel périodique
Controllability of a quantum particle in a 1D variable domain
We consider a quantum particle in a 1D infinite square potential well with variable length. It is a nonlinear control system in which the state is the wave function of the particle and the control is the length of the potential well. We prove the following controllability result : given close enough to an eigenstate corresponding to the length and close enough to another eigenstate corresponding to the length , there exists a continuous function with , such that and , and which...
Controllability of Schrödinger equations
One considers a quantum particle in a 1D moving infinite square potential well. It is a nonlinear control system in which the state is the wave function of the particle and the control is the acceleration of the potential well. One proves the local controllability around any eigenstate, and the steady state controllability (controllability between eigenstates) of this control system. In particular, the wave function can be moved from one eigenstate to another one, exactly and in finite time, by...
Controllablity of a quantum particle in a 1D variable domain
We consider a quantum particle in a 1D infinite square potential well with variable length. It is a nonlinear control system in which the state is the wave function ϕ of the particle and the control is the length l(t) of the potential well. We prove the following controllability result : given close enough to an eigenstate corresponding to the length l = 1 and close enough to another eigenstate corresponding to the length l=1, there exists a continuous function with T > 0, such that l(0)...
Convergence of gradient-based algorithms for the Hartree-Fock equations
The numerical solution of the Hartree-Fock equations is a central problem in quantum chemistry for which numerous algorithms exist. Attempts to justify these algorithms mathematically have been made, notably in [E. Cancès and C. Le Bris, Math. Mod. Numer. Anal. 34 (2000) 749–774], but, to our knowledge, no complete convergence proof has been published, except for the large-Z result of [M. Griesemer and F. Hantsch, Arch. Rational Mech. Anal. (2011) 170]. In this paper, we prove the convergence of...