Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Energy and Laplacian on Hanoi-type fractal quantum graphs   This article studies potential theory and spectral analysis on compact metric
spaces, which we refer to as fractal quantum graphs. These spaces can be
represented as a (possibly infinite) union of 1-dimensional intervals and a
totally disconnected (possibly uncountable) compact set, which roughly speaking
represents the set of junction points. Classical quantum graphs and fractal
spaces such as the Hanoi attractor are included among them. We begin with
proving the existence of a resistance form on the Hanoi attractor, and go on to
establish heat kernel estimates and upper and lower bounds on the eigenvalue
counting function of Laplacians corresponding to weakly self-similar measures
on the Hanoi attractor. These estimates and bounds rely heavily on the relation
between the length and volume scaling factors of the fractal. We then state and
prove a necessary and sufficient condition for the existence of a resistance
form on a general fractal quantum graph. Finally, we extend our spectral
results to a large class of weakly self-similar fractal quantum graphs.

8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex