Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sedentary quantum walks   Let $X$ be a graph with adjacency matrix $A$. The \textsl{continuous quantum
walk} on $X$ is determined by the unitary matrices $U(t)=\exp(itA)$. If $X$ is
the complete graph $K_n$ and $a\in V(X)$, then \[1-|U(t)_{a,a}|\le2/n. \] In a
sense, this means that a quantum walk on a complete graph stay home with high
probability. In this paper we consider quantum walks on cones over an
$\ell$-regular graph on $n$ vertices. We prove that if $\ell^2/n\to\infty$ as
$n$ increases, than a quantum walk that starts on the apex of the cone will
remain on it with probability tending to $1$ as $n$ increases. On the other
hand, if $\ell\le2$ we prove that there is a time $t$ such that local uniform
mixing occurs, i.e., all vertices are equally likely.
  We investigate when a quantum walk on strongly regular graph has a high
probability of "staying at home", producing large families of examples with the
stay-at-home property where the valency is small compared to the number of
vertices.

36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th