Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Magnetic quantum dots and rings in two dimensions   We consider the motion of electrons confined to a two dimensional plane with
an externally applied perpendicular inhomogeneous magnetic field, both with and
without a Coulomb potential. We find that as long as the magnetic field is
slowly-decaying, bound states in magnetic quantum dots are indeed possible.
Several example cases of such magnetic quantum dots are considered in which one
can find the eigenvalues and eigenfunctions in closed form, including two
hitherto unknown quasi-exactly solvable models treated with confluent and
biconfluent Heun polynomials. It is shown how a modulation of the strength of
the magnetic field can exclude magnetic vortex-like states, rotating with a
certain angular momenta and possessing a definite spin orientation, from
forming. This indicates one may induce localization-delocalization transitions
and suggests a mechanism for spin-separation.

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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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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: patt-sol
12
The categories of this paper are: nucl-th