Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Oscillatory Localization of Quantum Walks Analyzed by Classical Electric
  Circuits   We examine an unexplored quantum phenomenon we call oscillatory localization,
where a discrete-time quantum walk with Grover's diffusion coin jumps back and
forth between two vertices. We then connect it to the power dissipation of a
related electric network. Namely, we show that there are only two kinds of
oscillating states, called uniform states and flip states, and that the
projection of an arbitrary state onto a flip state is bounded by the power
dissipation of an electric circuit. By applying this framework to states along
a single edge of a graph, we show that low effective resistance implies
oscillatory localization of the quantum walk. This reveals that oscillatory
localization occurs on a large variety of regular graphs, including
edge-transitive, expander, and high degree graphs. As a corollary, high
edge-connectivity also implies localization of these states, since it is
closely related to electric resistance.

28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
2
The categories of this paper are: math
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas