Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: One-dimensional quantum walks via generating function and the CGMV
  method   We treat a quantum walk (QW) on the line whose quantum coin at each vertex
tends to be the identity as the distance goes to infinity. We obtain a limit
theorem that this QW exhibits localization with not an exponential but a
"power-law" decay around the origin and a "strongly" ballistic spreading called
bottom localization in this paper. This limit theorem implies the weak
convergence with linear scaling whose density has two delta measures at $x=0$
(the origin) and $x=1$ (the bottom) without continuous parts.

6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat