110 research outputs found
Bose Einstein condensate in the Lowest Landau Level : Hamiltonian dynamics
Ce texte est une prépublication de l'IRMAR.Dans un article antérieur avec A. Aftalion et X. Blanc, les propriétés d'hypercontractivité du semigroupe des dilatations dans des espaces de fonctions entières est apparu comme un outil essentiel de l'étude du modèle de plus bas niveau de Landau pour les condensats de Bose Einstein. Ce travail portait sur le problème stationnaire. Nous abordons ici la question de la dynamique Hamiltonienne et les problèmes de stabilité spectrale. A MODIFIED VERSION OF THIS PREPRINT HAS BEEN PUBLISHED IN REVIEWS IN MATHEMATICAL PHYSICS
Adiabatic evolution of 1D shape resonances: an artificial interface conditions approach
Artificial interface conditions parametrized by a complex number
are introduced for 1D-Schr\"odinger operators. When this complex parameter
equals the parameter of the complex deformation which unveils
the shape resonances, the Hamiltonian becomes dissipative. This makes possible
an adiabatic theory for the time evolution of resonant states for arbitrarily
large time scales. The effect of the artificial interface conditions on the
important stationary quantities involved in quantum transport models is also
checked to be as small as wanted, in the polynomial scale as
, according to .Comment: 60 pages, 13 figure
Boundary conditions and subelliptic estimates for geometric Kramers-Fokker-Planck operators on manifolds with boundaries
This article is concerned with maximal accretive realizations of geometric
Kramers-Fokker-Planck operators on manifolds with boundaries. A general class
of boundary conditions is introduced which ensures the maximal accretivity and
some global subelliptic estimates. Those estimates imply nice spectral
properties as well as exponential decay properties for the associated
semigroup. Admissible boundary conditions cover a wide range of applications
for the usual scalar Kramer-Fokker-Planck equation or Bismut's hypoelliptic
Laplacian.Comment: 186 page
Optimal non-reversible linear drift for the convergence to equilibrium of a diffusion
We consider non-reversible perturbations of reversible diffusions that do not
alter the invariant distribution and we ask whether there exists an optimal
perturbation such that the rate of convergence to equilibrium is maximized. We
solve this problem for the case of linear drift by proving the existence of
such optimal perturbations and by providing an easily implementable algorithm
for constructing them. We discuss in particular the role of the prefactor in
the exponential convergence estimate. Our rigorous results are illustrated by
numerical experiments
Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach: the case with boundary.
Prépublication 04-40, IRMAR, UMR-CNRS 6625, Université de Rennes 1 (Août 2004)This article is a continuation of previous works by Bovier-Eckhoff-Gayrard-Klein, Bovier-Gayrard-Klein and Helffer-Klein-Nier. It is concerned with the analysis of the exponentially small eigenvalues of a semiclassical Witten Laplacian. We consider here the case of riemanian manifolds with boundary with a Dirichlet realization of the Witten Laplacian. A modified version of this preprint has been published in Mémoires de la SMF vol. 105, (2006
Mean field limit for bosons and infinite dimensional phase-space analysis
International audienceThis article proposes the construction of Wigner measures in the infinite dimensional bosonic quantum field theory, with applications to the derivation of the mean field dynamics. Once these asymptotic objects are well defined, it is shown how they can be used to make connections between different kinds of results or to prove new ones
Mean field propagation of infinite dimensional Wigner measures with a singular two-body interaction potential
49 pagesInternational audienceWe consider the quantum dynamics of many bosons systems in the mean field limit with a singular pair-interaction potential, including the attractive or repulsive Coulombic case in three dimensions. By using a measure transportation technique, we show that Wigner measures propagate along the nonlinear Hartree flow. Such property was previously proved only for bounded potentials in our previous works with a slightly different strategy
Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach
Nous calculons de façon précise les premières valeurs propres, exponentiellement petites, du Laplacien de Witten sur les 0-formes. Ces quantités sont liées au taux de retour à l\'équilibre pour des processus stochastiques réversibles.Lápproche proposée ici repose sur la structure du complexe de Witten et donne des résultats plus précis et généraux que les méthodes probabilistes
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