arXiv subjects
Publications and source records attributed to T. Christiansen.
We report on the status and history of the CMS commissioning, together with selected results from cosmic-ray muon data. The second part focuses on strategies for optimizing the reconstruction of jets, missing transverse energy and photons for early standard model measurements at ATLAS and CMS with the first collision data from the Large Hadron Collider at CERN.
We show that the resonance counting function for a Schrödinger operator has maximal order of growth for generic sets of real-valued, or complex-valued, $L^\infty$-compactly supported potentials.
In dimension $d\geq 3$, we give examples of nontrivial, compactly supported, complex-valued potentials such that the associated Schrödinger operators have no resonances. If $d=2$, we show that there are potentials with no resonances away from the origin. These Schrödinger operators are isophasal and have the same scattering phase as the Laplacian on $\Real^d$. In odd dimensions $d\geq 3$ we study the fundamental solution of the wave equation perturbed by such a potential. If the space variables are held fixed, it is super-exponentially decaying in time.
We study resonances associated to Schrödinger operators with compactly supported potentials on ${\mathbb R}^d$, $d\geq3$, odd. We consider compactly supported potentials depending holomorphically on a complex parameter $z$. For certain such families, for all $z$ except those in a pluripolar set, the associated resonance-counting function has order of growth $d$. Our proofs use some results from several complex variables.
We study certain resonance-counting functions for potential scattering on infinite cylinders or half-cylinders. Under certain conditions on the potential, we obtain asymptotics of the counting functions, with an explicit formula for the constant appearing in the leading term.
We consider resonances associated to the operator $-\frac{d^2}{dx^2}+V(x)$, where $V(x)=V_+$ if $x>x_M$ and $V(x)=V_-$ if $x<-x_M$, with $V_+\not = V_-$. We obtain asymptotics of the resonance-counting function in several regions. Moreover, we show that in several situations, the resonances, $V_+$, and $V_-$ determine $V$ uniquely up to translation.
We prove some sharp upper bounds on the number of resonances associated with the Laplacian, or Laplacian plus potential, on a manifold with infinite cylidrical ends.