Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum graph vertices with permutation-symmetric scattering
  probabilities   Boundary conditions in quantum graph vertices are generally given in terms of
a unitary matrix $U$. Observing that if $U$ has at most two eigenvalues, then
the scattering matrix $\mathcal{S}(k)$ of the vertex is a linear combination of
the identity matrix and a fixed Hermitian unitary matrix, we construct vertex
couplings with this property: For all momenta $k$, the transmission probability
from the $j$-th edge to $\ell$-th edge is independent of $(j,\ell)$, and all
the reflection probabilities are equal. We classify these couplings according
to their scattering properties, which leads to the concept of generalized
$\delta$ and $\delta'$ couplings.

29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con