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math-ph2018
Positive Hausdorff dimensional spectrum for the critical almost Mathieu operator
Bernard Helffer, Qinghui Liu, Yanhui Qu +1
We show that there exists a dense set of frequencies with positive Hausdorff dimension for which the Hausdorff dimension of the spectrum of the critical almost Mathieu operator is…
math-ph2018
The spectrum of a Schrödinger operator in a wire-like domain with a purely imaginary degenerate potential in the semiclassical limit
Yaniv Almog, Bernard Helffer
Consider a two-dimensional domain shaped like a wire, not necessarily of uniform cross section. Let denote an electric potential driven by a voltage drop between the conducting…