Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the existence of impurity bound excitons in one-dimensional systems
  with zero range interactions   We consider a three-body one-dimensional Schr\"odinger operator with zero
range potentials, which models a positive impurity with charge $\kappa > 0$
interacting with an exciton. We study the existence of discrete eigenvalues as
$\kappa$ is varied. On one hand, we show that for sufficiently small $\kappa$
there exists a unique bound state whose binding energy behaves like $\kappa^4$,
and we explicitly compute its leading coefficient. On the other hand, if
$\kappa$ is larger than some critical value then the system has no bound
states.

23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an