Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuous deformations of the Grover walk preserving localization   The three-state Grover walk on a line exhibits the localization effect
characterized by a non-vanishing probability of the particle to stay at the
origin. We present two continuous deformations of the Grover walk which
preserve its localization nature. The resulting quantum walks differ in the
rate at which they spread through the lattice. The velocities of the left and
right-traveling probability peaks are given by the maximum of the group
velocity. We find the explicit form of peak velocities in dependence on the
coin parameter. Our results show that localization of the quantum walk is not a
singular property of an isolated coin operator but can be found for entire
families of coins.

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The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
9
The categories of this paper are: nlin
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The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph