Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum graph as a quantum spectral filter   We study the transmission of a quantum particle along a straight
input--output line to which a graph $\Gamma$ is attached at a point. In the
point of contact we impose a singularity represented by a certain properly
chosen scale-invariant coupling with a coupling parameter $\alpha$. We show
that the probability of transmission along the line as a function of the
particle energy tends to the indicator function of the energy spectrum of
$\Gamma$ as $\alpha\to\infty$. This effect can be used for a spectral analysis
of the given graph $\Gamma$. Its applications include a control of a
transmission along the line and spectral filtering. The result is illustrated
with an example where $\Gamma$ is a loop exposed to a magnetic field. Two more
quantum devices are designed using other special scale-invariant vertex
couplings. They can serve as a band-stop filter and as a spectral separator,
respectively.

27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys