Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Localization of two-dimensional quantum walks defined by generalized
  Grover coins   In this paper, we study the localization phenomena of discrete-time coined
quantum walks (DTQWs) on two-dimensional lattices when the coins are
permutative orthogonal (real) matrices of order $4 \times 4.$ First, we provide
a complete characterization of all complex, real and rational permutative
orthogonal matrices of dimension $4\times 4$; and consequently we determine new
chains of groups of orthogonal matrices. Next, we determine matrix spaces
generated by certain permutation matrices of order $4\times 4$ such that
orthogonal matrices in these spaces are permutative matrices or direct sum of
permutative matrices up to permutation of rows and columns. However, we provide
an example of a matrix space which contains orthogonal matrices that are
neither of these forms. Then we establish that the localization phenomena of
Grover walk at initial position corresponding to canonical initial coin states
is extended to the proposed quantum walks on two-dimensional infinite lattice
with generalized Grover coins, which need not be true for any coin which is a
permutative orthogonal (real) matrix.

30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph