Groupes quantiques
Group-valued measures on coarse-grained quantum logics
In it was shown that a (real) signed measure on a cyclic coarse-grained quantum logic can be extended, as a signed measure, over the entire power algebra. Later () this result was re-proved (and further improved on) and, moreover, the non-negative measures were shown to allow for extensions as non-negative measures. In both cases the proof technique used was the technique of linear algebra. In this paper we further generalize the results cited by extending group-valued measures on cyclic coarse-grained...
Half-delocalization of eigenfunctions for the Laplacian on an Anosov manifold
We study the high-energy eigenfunctions of the Laplacian on a compact Riemannian manifold with Anosov geodesic flow. The localization of a semiclassical measure associated with a sequence of eigenfunctions is characterized by the Kolmogorov-Sinai entropy of this measure. We show that this entropy is necessarily bounded from below by a constant which, in the case of constant negative curvature, equals half the maximal entropy. In this sense, high-energy eigenfunctions are at least half-delocalized....
Hall's transformation via quantum stochastic calculus
It is well known that Hall's transformation factorizes into a composition of two isometric maps to and from a certain completion of the dual of the universal enveloping algebra of the Lie algebra of the initial Lie group. In this paper this fact will be demonstrated by exhibiting each of the maps in turn as the composition of two isometries. For the first map we use classical stochastic calculus, and in particular a stochastic analogue of the Dyson perturbation expansion. For the second map we make...
Hamiltonian identification for quantum systems: well-posedness and numerical approaches
This paper considers the inversion problem related to the manipulation of quantum systems using laser-matter interactions. The focus is on the identification of the field free Hamiltonian and/or the dipole moment of a quantum system. The evolution of the system is given by the Schrödinger equation. The available data are observations as a function of time corresponding to dynamics generated by electric fields. The well-posedness of the problem is proved, mainly focusing on the uniqueness of the...
Hamiltonian reduction and quantization on symplectic manifolds.
Hamiltonian systems inspired by the Schrödinger equation.
Hamiltonians for systems of N particles interacting through point interactions
Hamiltonians with zero-range interactions supported by a brownian path
Harmonic maps of the hyperbolic space and development of singularities in wave maps and Yang-Mills fields
Harmonic superfields in supersymmetric quantum mechanics.
Hartogs phenomena for Hermitian vector bundles
Hartree-Fock theory in nuclear physics
Heat trace asymptotics on noncommutative spaces.
Heavy molecules in the strong magnetic field
Heisenberg uncertainty relation in quantum Liouville equation.
Heisenberg's picture and non commutative geometry of the semi classical limit in quantum mechanics
Hermite -polynomials and -oscillators
Hidden symmetries of integrable systems in Yang-Mills theory and Kähler geometry
Hidden symmetry from supersymmetry in one-dimensional quantum mechanics.