Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ring chains with vertex coupling of a preferred orientation   We consider a family of Schr\"odinger operators supported by a periodic chain
of loops connected either tightly or loosely through connecting links of the
length $\ell>0$ with the vertex coupling which is non-invariant with respect to
the time reversal. The spectral behavior of the model illustrates that the
high-energy behavior of such vertices is determined by the vertex parity. The
positive spectrum of the tightly connected chain covers the entire halfline
while the one of the loose chain is dominated by gaps. In addition, there is a
negative spectrum consisting of an infinitely degenerate eigenvalue in the
former case, and of one or two absolutely continuous bands in the latter.
Furthermore, we discuss the limit $\ell\to 0$ and show that while the spectrum
converges as a set to that of the tight chain, as it should in view of a result
by Berkolaiko, Latushkin, and Sukhtaiev, this limit is rather non-uniform.

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The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex