Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum random walk in periodic potential on a line   We investigated the discrete-time quantum random walks on a line in periodic
potential. The probability distribution with periodic potential is more complex
compared to the normal quantum walks, and the standard deviation $\sigma$ has
interesting behaviors for different period $q$ and parameter $\theta$. We
studied the behavior of standard deviation with variation in walk steps,
period, and $\theta$. The standard deviation increases approximately linearly
with $\theta$ and decreases with $1/q$ for $\theta\in(0,\pi/4)$, and increases
approximately linearly with $1/q$ for $\theta\in[\pi/4,\pi/2)$. When $q=2$, the
standard deviation is lazy for $\theta\in[\pi/4+n\pi,3\pi/4+n\pi],n\in Z$.

27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
2
The categories of this paper are: math
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin