2-magnon scattering in the Heisenberg model
A mathematical introduction to the Wigner formulation of quantum mechanics
The paper is devoted to review, from a mathematical point of view, some fundamental aspects of the Wigner formulation of quantum mechanics. Starting from the axioms of quantum mechanics and of quantum statistics, we justify the introduction of the Wigner transform and eventually deduce the Wigner equation.
A minimax principle for eigenvalues in spectral gaps: Dirac operators with Coulomb potentials.
A new phase space localization technique with application to the sum of negative eigenvalues of Schrödinger operators
A single scale infinite volume expansion for three dimensional many Fermion Green's functions.
About poles of the resolvent, in a model for a harmonic oscillator coupled with massless scalar bosons
absence de résonance près du réel pour l’opérateur de Schrödinger
On donne dans cet exposé des bornes inférieures universelles, en limite semiclassique, de la hauteur des résonances de forme associées aux opérateurs de Schrödinger à l’extérieur d’obstacles avec des conditions au bord de Dirichlet ou de Neumann et des potentiels analytiquement dilatables et tendant vers à l’infini. Ces bornes inférieures sont exponentiellement petites par rapport à la constante de Planck.
Absence of point spectrum for a class of discrete Schrödinger operators with quasiperiodic potential.
Abstract quasi-variational inequalities of elliptic type and applications
A class of quasi-variational inequalities (QVI) of elliptic type is studied in reflexive Banach spaces. The concept of QVI was earlier introduced by A. Bensoussan and J.-L. Lions [2] and its general theory has been developed by many mathematicians, for instance, see [6, 7, 9, 13] and a monograph [1]. In this paper we give a generalization of the existence theorem established in [14]. In our treatment we employ the compactness method along with a concept of convergence of nonlinear multivalued operators...
An infinite level atom coupled to a heat bath.
Anomalous quantum transport in presence of self-similar spectra
Berezin transforms and group representations.
Bounds on the zeros of a renormalization group fixed point.
Calculation of the Hall conductivity by Abel limit
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...
Charge transfer scatteringin a constant electric field
We prove the asymptotic completeness of the quantum scattering for a Stark Hamiltonian with a time dependent interaction potential, created by N classical particles moving in a constant electric field.
Circular operators related to some quantum observables
Circular operators related to the operator of multiplication by a homomorphism of a locally compact abelian group and its restrictions are completely characterized. As particular cases descriptions of circular operators related to various quantum observables are given.
Classical and quantum scattering for Stark hamiltonians with slowly decaying potentials
Combinatorial approach to Baker-Campbell-Hausdorff exponents
Construction of Non-Linear Local Quantum Processes.