Currently displaying 1 – 4 of 4

Showing per page

Order by Relevance | Title | Year of publication

Localization for Schrödinger operators with Poisson random potential

Abel Klein;  Peter Hislop;  François Germinet — 2007

Journal of the European Mathematical Society

We prove exponential and dynamical localization for the Schr¨odinger operator with a nonnegative Poisson random potential at the bottom of the spectrum in any dimension. We also conclude that the eigenvalues in that spectral region of localization have finite multiplicity. We prove similar localization results in a prescribed energy interval at the bottom of the spectrum provided the density of the Poisson process is large enough.

On the distribution of resonances for some asymptotically hyperbolic manifolds

R. G. Froese;  Peter D. Hislop — 2000

Journées équations aux dérivées partielles

We establish a sharp upper bound for the resonance counting function for a class of asymptotically hyperbolic manifolds in arbitrary dimension, including convex, cocompact hyperbolic manifolds in two dimensions. The proof is based on the construction of a suitable paramatrix for the absolute S -matrix that is unitary for real values of the energy. This paramatrix is the S -matrix for a model laplacian corresponding to a separable metric near infinity. The proof of the upper bound on the resonance...

Page 1

Download Results (CSV)