Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Notes on Inhomogeneous Quantum Walks   We study a class of discrete-time quantum walks with inhomogeneous coins
defined in [Y. Shikano and H. Katsura, Phys. Rev. E {\bf 82}, 031122 (2010)].
We establish symmetry properties of the spectrum of the evolution operator,
which resembles the Hofstadter butterfly.

17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: stat
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
1
The categories of this paper are: cs
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th