27 research outputs found
Resonances for "large" ergodic systems in one dimension: a review
The present note reviews recent results on resonances for one-dimensional
quantum ergodic systems constrained to a large box. We restrict ourselves to
one dimensional models in the discrete case. We consider two type of ergodic
potentials on the half-axis, periodic potentials and random potentials. For
both models, we describe the behavior of the resonances near the real axis for
a large typical sample of the potential. In both cases, the linear density of
their real parts is given by the density of states of the full ergodic system.
While in the periodic case, the resonances distribute on a nice analytic curve
(once their imaginary parts are suitably renormalized), In the random case, the
resonances (again after suitable renormalization of both the real and imaginary
parts) form a two dimensional Poisson cloud
Generalized eigenfunctions and spectral theory for strongly local Dirichlet forms
We present an introduction to the framework of strongly local Dirichlet forms
and discuss connections between the existence of certain generalized
eigenfunctions and spectral properties within this framework. The range of
applications is illustrated by a list of examples
On the Solvability in the Sense of Sequences for Some Non-Fredholm Operators Related to the Anomalous Diffusion
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