Matrices de diffusion pour l'opérateur de Schrödinger en présence d'un champ magnétique. Phénomène de Aharonov-Bohm
Matrici simmetriche quantiche e teoria delle rappresentazioni
Matrix elements and highest weight Wigner coefficients of
Matrix elements for sum of power-law potentials in quantum mechanic using generalized hypergeometric functions.
Matrix representation of finite effect algebras
In this paper we present representation of finite effect algebras by matrices. For each non-trivial finite effect algebra we construct set of matrices in such a way that effect algebras and are isomorphic if and only if . The paper also contains the full list of matrices representing all nontrivial finite effect algebras of cardinality at most .
Max Born a vznik kvantovej mechaniky
Maximal Monotonicity of Operators with Sufficiently Large Domain and Application to the Hartree Problem.
Maximal violation of Bell's inequalities for algebras of observables in tangent spacetime regions
Maximum entropy wave functions.
Mean-field evolution of fermionic systems
We study the dynamics of interacting fermionic systems, in the mean-field regime. We consider initial states which are close to quasi-free states and prove that, under suitable assumptions on the inital data and on the many-body interaction, the quantum evolution of the system is approximated by a time-dependent quasi-free state. In particular we prove that the evolution of the reduced one-particle density matrix converges, as the number of particles goes to infinity, to the solution of the time-dependent...
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)...
Measure solutions for semilinear evolution equations with polynomial growth and their optimal control
In this paper we introduce a new concept of generalized solutions generalizing the notion of relaxed solutions recently introduced by Fattorini. We present some results on the question of existence of generalized or measure valued solutions for semilinear evolution equations on Banach spaces with polynomial nonlinearities. The results are illustrated by two examples one of which arises in nonlinear quantum mechanics. The results are then applied to some control problems.
Measures connected with Bargmann's representation of the q-commutation relation for q > 1
Classical Bargmann’s representation is given by operators acting on the space of holomorphic functions with scalar product . We consider the problem of representing the functional F as a measure. We prove the existence of such a measure for q > 1 and investigate some of its properties like uniqueness and radiality.
Measures on orthomodular vector space lattices
Mécanique quantique sur le tore et dégénérescences dans le spectre
Mechanical analogy for the wave-particle: Helix on a vortex filament.
Mesures limites pour l’équation de Helmholtz dans le cas non captif
Cet article est consacré à l’étude des mesures limites associées à la solution de l’équation de Helmholtz avec un terme source se concentrant en un point. Le potentiel est supposé et l’opérateur non-captif. La solution de l’équation de Schrödinger semi-classique s’écrit alors micro-localement comme somme finie de distributions lagrangiennes. Sous une hypothèse géométrique, qui généralise l’hypothèse du viriel, on en déduit que la mesure limite existe et qu’elle vérifie des propriétés standard....
Mesures semi-classiques et croisement de modes
Metal-insulator transition for the almost Mathieu operator.
Metaplectic quantization of the moduli spaces of flat and parabolic bundles.