Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perfect state transfer on graphs with a potential   In this paper we study quantum state transfer (also called quantum tunneling)
on graphs when there is a potential function on the vertex set. We present two
main results. First, we show that for paths of length greater than three, there
is no potential on the vertices of the path for which perfect state transfer
between the endpoints can occur. In particular, this answers a question raised
by Godsil in Section 20 of [8]. Second, we show that if a graph has two
vertices that share a common neighborhood, then there is a potential on the
vertex set for which perfect state transfer will occur between those two
vertices. This gives numerous examples where perfect state transfer does not
occur without the potential, but adding a potential makes perfect state
transfer possible. In addition, we investigate perfect state transfer on graph
products, which gives further examples where perfect state transfer can occur.

10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys