52 research outputs found
A strong operator topology adiabatic theorem
We prove an adiabatic theorem for the evolution of spectral data under a weak
additive perturbation in the context of a system without an intrinsic time
scale. For continuous functions of the unperturbed Hamiltonian the convergence
is in norm while for a larger class functions, including the spectral
projections associated to embedded eigenvalues, the convergence is in the
strong operator topology.Comment: 15 pages, no figure
H\"older equicontinuity of the integrated density of states at weak disorder
H\"older continuity, , with
a constant independent of the disorder strength is proved for the
integrated density of states associated to a discrete random
operator consisting of a translation invariant hopping
matrix and i.i.d. single site potentials with an absolutely
continuous distribution, under a regularity assumption for the hopping term.Comment: 15 Pages, typos corrected, comments and ref. [1] added, theorems 3,4
combine
Moment analysis for localization in random Schrödinger operators
We study localization effects of disorder on the spectral and dynamical properties of Schrödinger operators with random potentials. The new results include exponentially decaying bounds on the transition amplitude and related projection kernels, including in the mean. These are derived through the analysis of fractional moments of the resolvent, which are finite due to the resonance-diffusing effects of the disorder. The main difficulty which has up to now prevented an extension of this method to the continuum can be traced to the lack of a uniform bound on the Lifshitz-Krein spectral shift associated with the local potential terms. The difficulty is avoided here through the use of a weak-L1 estimate concerning the boundary-value distribution of resolvents of maximally dissipative operators, combined with standard tools of relative compactness theor
Observing the Symmetry of Attractors
We show how the symmetry of attractors of equivariant dynamical systems can
be observed by equivariant projections of the phase space. Equivariant
projections have long been used, but they can give misleading results if used
improperly and have been considered untrustworthy. We find conditions under
which an equivariant projection generically shows the correct symmetry of the
attractor.Comment: 28 page LaTeX document with 9 ps figures included. Supplementary
color figures available at http://odin.math.nau.edu/~jws
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