4,391 research outputs found
Exact scaling transform for a unitary quantum gas in a time dependent harmonic potential
A unitary quantum gas is a gas of quantum particles with a binary interaction
of infinite scattering length and negligible range. It has been produced in
recent experiments with gases of fermionic atoms by means of a Feshbach
resonance. Using the Fermi pseudo-potential model for the atomic interaction,
we show that the time evolution of such a gas in an isotropic three-dimensional
time dependent harmonic trap is exactly given by a gauge and scaling transform.Comment: submitted 23 March 200
Sur la théorie du potentiel dans les domaines de John
Using rather elementary and direct methods, we first recover and add on some results of Aikawa-Hirata-Lundh about the Martin boundary of a John domain. In particular we answer a question raised by these authors. Some applications are given and the case of more general second order elliptic operators is also investigated. In the last parts of the paper two potential theoretic results are shown in the framework of uniform domains or the framework of hyperbolic manifolds
Laplaciens de graphes infinis I Graphes m\'etriquement complets
We introduce the weighted graph Laplacian and the notion of Schr\"odinger
operator on a locally finite weighted graph . Concerning essential
self-adjointness, we extend Wojciechowski's and Dodziuk's results for graphs
with vertex constant weight. The main result in this work states that on any
metrically complete weighted graph with bounded degree, the Laplacian is
essentially self-adjoint and the same holds for the Schr\"odinger operator
provided the associated quadratic form is bounded from below. We construct for
the proof a strictly positive and harmonic function which allows us to write
any Schr\"odinger operator as a weighted graph Laplacian modulo a unitary
transform
Théorème ergodique pour cocycle harmonique, applications au milieu aléatoire. Ergodic theorem for harmonic cocycle, applications in random environment.
In this work we prove the pointwise ergodic theorem for harmonic degree 1 cocycle of a measurable stationary action of Z^d on a probability space. In a precedent paper Boivin and Derriennic (1991) studied this theorem for not necessarily harmonic cocycles. The harmonic hypothesis allows, in the elliptic case, to change the integrability condition to L^2, while Boivin and Derriennic showed that the optimum condition in the non-harmonic case is the finiteness of Lorentz's norm L_{d,1}. They showed in particular that L^d is not enough. Berger and Biskup published in 2007 a paper on the harmonic not elliptic case, but only in dimension d=2. Finally, applications of this theorem in random media are presented
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