Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometrical aspects of quantum walks on random two-dimensional
  structures   We study the transport properties of continuous-time quantum walks (CTQW)
over finite two-dimensional structures with a given number of randomly placed
bonds and with different aspect ratios (AR). Here, we focus on the transport
from, say, the left side to the right side of the structure where absorbing
sites are placed. We do so by analyzing the long-time average of the survival
probability of CTQW. We compare the results to the classical continuous-time
random walk case (CTRW). For small AR (landscape configurations) we observe
only small differences between the quantum and the classical transport
properties, i.e., roughly the same number of bonds is needed to facilitate the
transport. However, with increasing AR (portrait configurations) a much larger
number of bonds is needed in the CTQW case than in the CTRW case. While for
CTRW the number of bonds needed decreases when going from small AR to large AR,
for CTRW this number is large for small AR, has a minimum for the square
configuration, and increases again for increasing AR. We corroborate our
findings for large AR by showing that the corresponding quantum eigenstates are
strongly localized in situations in which the transport is facilitated in the
CTRW case.

23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom