6 research outputs found
Exponential decay of Laplacian eigenfunctions in domains with branches
The behavior of Laplacian eigenfunctions in domains with branches is
investigated. If an eigenvalue is below a threshold which is determined by the
shape of the branch, the associated eigenfunction is proved to exponentially
decay inside the branch. The decay rate is twice the square root of the
difference between the threshold and the eigenvalue. The derived exponential
estimate is applicable for arbitrary domains in any spatial dimension.
Numerical simulations illustrate and further extend the theoretical estimate
Low lying spectrum of weak-disorder quantum waveguides
We study the low-lying spectrum of the Dirichlet Laplace operator on a
randomly wiggled strip. More precisely, our results are formulated in terms of
the eigenvalues of finite segment approximations of the infinite waveguide.
Under appropriate weak-disorder assumptions we obtain deterministic and
probabilistic bounds on the position of the lowest eigenvalue. A Combes-Thomas
argument allows us to obtain so-called 'initial length scale decay estimates'
at they are used in the proof of spectral localization using the multiscale
analysis.Comment: Accepted for publication in Journal of Statistical Physics
http://www.springerlink.com/content/0022-471