Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Superconductivity by Berry connection from many-body wave functions:
  revisit to Andreev$-$Saint-James reflection and Josephson effect   Although the standard theory of superconductivity based on the BCS theory is
a successful one, several experimental results indicate the necessity for a
fundamental revision. We argue that the revision is on the origin of the phase
variable for superconductivity; this phase appears as a consequence of the
electron-pairing in the standard theory, but its origin is a Berry connection
arising from many-body wave functions.
  When this Berry connection is non-trivial, it gives rise to a collective mode
that generates supercurrent; this collective mode creates number-changing
operators for particles participating in this mode, and these number-changing
operators stabilize the superconducting state by exploiting the Cooper
instability. In the new theory, the role of the electron-pairing is to
stabilize the nontrivial Berry connection; it is not the cause of
superconductivity.
  In BCS superconductors, however, the simultaneous appearance of the
nontrivial Berry connection and the electron-pairing occurs. Therefore, the
electron-pairing amplitude can be used as an order parameter for the
superconducting state. We revisit the Andreev$-$Saint-James reflection and the
Josephson effect. They are explained as consequence of the presence of the
Berry connection. Bogoliubov quasiparticles are replaced by the particle-number
conserving Bogoliubov excitations that describe the transfer of electrons
between the collective mod and single particle mode.

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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn