Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inverse scattering at fixed energy for radial magnetic Schr{\"o}dinger
  operators with obstacle in dimension two   We study an inverse scattering problem at fixed energy for radial magnetic
Schr{\"o}dinger operators on R^2 \ B(0, r\_0), where r\_0 is a positive and
arbitrarily small radius. We assume that the magnetic potential A satisfies a
gauge condition and we consider the class C of smooth, radial and compactly
supported electric potentials and magnetic fields denoted by V and B
respectively. If (V, B) and (\tilde{V} , \tilde{B}) are two couples belonging
to C, we then show that if the corresponding phase shifts $\delta$\_l and
\tilde{$\delta$}\_l (i.e. the scattering data at fixed energy) coincide for all
l $\in$ L, where L $\subset$ N^$\star$ satisfies the M{\"u}ntz condition
\sum\_{l$\in$L} \frac{1}{l} = +$\infty$, then V (x) = \tilde{V}(x) and B(x) =
\tilde{B}(x) outside the obstacle B(0, r\_0). The proof use the Complex Angular
Momentum method and is close in spirit to the celebrated B{\"o}rg-Marchenko
uniqueness Theorem.

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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
16
The categories of this paper are: stat
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The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
1
The categories of this paper are: cs