Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cooper pair ring model   The superconducting state starts to collapse when the externally applied
magnetic field exceeds the Meissner-Ochsenfeld critical field, Bc,MO, which in
type-I superconductors is the thermodynamic critical field, while in type-II
superconductors this field is the lower critical field. Here we show that both
critical fields can be described by the universal equation of
$B$$_{c,MO}$=$\mu$$_0$$n$$\mu$$_B$$ln(1+2$$^{0.5}$$\kappa$), where $\mu$$_0$ is
the magnetic permeability of free space, $n$ is the Cooper pairs density, and
$\mu$$_B$ is the Bohr magneton, and $\kappa$ is the Ginzburg-Landau parameter.
As a result, the Meissner-Ochsenfeld field can be defined as the field at which
each Cooper pair exhibits the diamagnetic moment of one Bohr magneton with a
multiplicative pre-factor of $ln(1+2$$^{0.5}$$\kappa$). In the two-dimensional
case this implies that the Cooper pair center of mass is spatially confined
within a ring with inner radius $\xi$ and outer radius of
$\xi$+2$^{0.5}$$\lambda$, where $\xi$ is the coherence length and $\lambda$ is
the London penetration depth. This means that the superconducting transition is
associated not only with the charge carrier pairing, but that the pairs exhibit
a new topological state with genus 1.

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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph