A note on spectrum and quantum dynamics

Abstract

We show, in the same vein of Simon's Wonderland Theorem, that, typically in Baire's sense, the rates with whom the solutions of the Schrödinger equation escape, in time average, from every finite-dimensional subspace, depend on subsequences of time going to infinite.

Hydrogen atom bound states whose spectral measures have positive upper fractal dimensions

“…Remark 2.3. To put our work into perspective, we note that establishing bounds on the exponents β ∓ ψ (p, B) in purely spectral terms (that is, without making reference to a specific form of a selfadjoint operator T ) is an important problem, that has attracted significant interest (see [1,4,5,6,7,9,15,16,17,19,23]). In this context, we emphasize that the lower bounds in Theorem 2.1 only depend on the form of the Hydrogen atom eigenvalues (see also Remark 1.1).…”