Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Resonance free domain for a system of Schr\"odinger operators with
  energy-level crossings   We consider a $2\times 2$ system of 1D semiclassical differential operators
with two Schr\"odinger operators in the diagonal part and small interactions of
order $h^\nu$ in the off-diagonal part, where $h$ is a semiclassical parameter
and $\nu$ is a constant larger than $1/2$. We study the absence of resonance
near a non-trapping energy for both Schr\"odinger operators in the presence of
crossings of their potentials. The width of resonances is estimated from below
by $Mh\log(1/h)$ and the coefficient $M$ is given in terms of the directed
cycles of the generalized bicharacteristics induced by two Hamiltonians.

22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org