Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scattering by a toroidal coil   In this paper we consider the Schr\"odinger operator in ${\mathbb R}^3$ with
a long-range magnetic potential associated to a magnetic field supported inside
a torus ${\mathbb{T}}$. Using the scheme of smooth perturbations we construct
stationary modified wave operators and the corresponding scattering matrix
$S(\lambda)$. We prove that the essential spectrum of $S(\lambda)$ is an
interval of the unit circle depending only on the magnetic flux $\phi$ across
the section of $\mathbb{T}$. Additionally we show that, in contrast to the
Aharonov-Bohm potential in ${\mathbb{R}}^2$, the total scattering cross-section
is always finite. We also conjecture that the case treated here is a typical
example in dimension 3.

3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an