Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the lowest energy of a 3D magnetic hamiltonian with axisymmetric
  potential   We study the bottom of the spectrum of a magnetic hamiltonian with
axisymmetrical potential in R3. The associated magnetic field is planar,
unitary and non-constant. The problem reduces to a 1D-family of singular
Sturm-Liouville operators on the half-line. We study to associated band
functions and we compare it to the "de Gennes" operators arising in the study
of a 2D-hamiltonian with monodimensional, odd and discontinuous magnetic field.
We show in particular that the lowest energy is higher in dimension 3.

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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc