Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The spectrum of the Schr\"{o}dinger Hamiltonian for trapped particles in
  a cylinder with a topological defect perturbed by two attractive delta
  interactions   In this paper we exploit the technique used in \cite{A}-\cite{5b} to deal
with delta interactions in a rigorous way in a curved spacetime represented by
a cosmic string along the $z$ axis. This mathematical machinery is applied in
order to study the discrete spectrum of a point-mass particle confined in an
infinitely long cylinder with a conical defect on the $z$ axis and perturbed by
two identical attractive delta interactions symmetrically situated around the
origin. We derive a suitable approximate formula for the total energy. As a
consequence, we found the existence of a mixing of states with positive or zero
energy with the ones with negative energy (bound states). This mixture depends
on the radius $R$ of the trapping cylinder. The number of quantum bound states
is an increasing function of the radius $R$. It is also interesting to note the
presence of states with zero total energy (quasi free states). Apart from the
gravitational background, the model presented in this paper is of interest in
the context of nanophysics and graphene modeling. In particular, the graphene
with double layer in this framework, with the double layer given by the
aforementioned delta interactions and the string on the $z-$axis modeling
topological defects connecting the two layers. As a consequence of these
setups, we obtain the usual mixture of positive and negative bound states
present in the graphene literature.

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The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th