Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuum Schr\"odinger Operators Associated With Aperiodic Subshifts   We study Schr\"odinger operators on the real line whose potentials are
generated by an underlying ergodic subshift over a finite alphabet and a rule
that replaces symbols by compactly supported potential pieces. We first develop
the standard theory that shows that the spectrum and the spectral type are
almost surely constant, and that identifies the almost sure absolutely
continuous spectrum with the essential closure of the set of energies with
vanishing Lyapunov exponent. Using results of Damanik-Lenz and
Klassert-Lenz-Stollmann, we also show that the spectrum is a Cantor set of zero
Lebesgue measure if the subhift satisfies the Boshernitzan condition and the
potentials are aperiodic and irreducible. We then study the case of the
Fibonacci subshift in detail and prove results for the local Hausdorff
dimension of the spectrum at a given energy in terms of the value of the
associated Fricke-Vogt invariant. These results are elucidated for some simple
choices of the local potential pieces, such as piecewise constant ones and
local point interactions. In the latter special case, our results explain the
occurrence of so-called pseudo bands, which have been pointed out in the
physics literature.

24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
16
The categories of this paper are: stat
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an