Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Periodic spectrum of $n$-cubic quantun graphs   We study the spectrum of some periodic differential operators, in particular
the periodic Schr\"{o}dinger operator acting on infinite $n$-cubic graphs.
Using Floquet-Bloch theory, we derive and analyze on the dispersion relations
of the periodic quantum graph generated by 2-dimensional rectangles, and also
$n$-cubes. Our proof is analytic. These dispersion relations define the spectra
of the associated periodic operator, thus facilitating further analysis of the
spectra.

22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph