Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Intertwining operators between one-dimensional homogeneous quantum walks   The subject of this paper is a kind of dynamical systems called quantum
walks. We study one-dimensional homogeneous analytic quantum walks U. We
explain how to identify the space of all the uniform intertwining operators
between these walks. We can also determine whether U can be realized by a (not
necessarily homogeneous) continuous-time uniform quantum walk on Z. Several
examples of quantum walks, which can not be realized by continuous-time uniform
quantum walks, are presented. The 4-state Grover walk is one of them. Before
stating the main theorems, we clarify the definition of one-dimensional quantum
walks. For the first half of this paper, we study basic properties of
one-dimensional quantum walks, which are not necessarily homogeneous. An
equivalence relation between quantum walks called similarity is also
introduced. This allows us to manipulate quantum walks in a flexible manner.

9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph