Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Proximity effect in the presence of Coulomb interaction and magnetic
  field   We consider a small metallic grain coupled to a superconductor by a tunnel
contact. We study the interplay between proximity and charging effects in the
presence of the external magnetic field. Employing the adiabatic approximation
we develop a self-consistent theory valid for an arbitrary ratio of proximity
and Coulomb strength. The magnetic field suppresses the proximity-induced
minigap in an unusual way. We find the phase diagram of the grain in the
charging energy - magnetic field plane. Two distinct states exist with
different values and magnetic field dependences of the minigap. The first-order
phase transition occurs between these two minigapped states. The transition to
the gapless state may occur by the first- or second-order mechanism depending
on the charging energy. We also calculate the tunneling density of states in
the grain. The energy dependence of this quantity demonstrates two different
gaps corresponding to the Coulomb and proximity effects. These gaps may be
separated in sufficiently high magnetic field.

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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg