Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $K$ dependent exchange interaction of the $1S$ ortho exciton in Cu$_2$O   When treating the exchange interaction of Wannier excitons, usually only the
leading terms of the analytic and the nonanalytic exchange interaction are
considered. However, higher order terms can lead to a splitting of exciton
states, for which reason a splitting of the $1S$~exciton in cuprous oxide
$\left(\mathrm{Cu_{2}O}\right)$ depending on its total momentum $\hbar K$ has
been attributed to a $K$ dependent analytic exchange interaction by Dasbach et
al [Phys. Rev. Lett. 91, 107401 (2003)]. Going beyond the common treatment of
the exchange interaction, we derive the correct expressions for these $K$
dependent higher order terms using $\boldsymbol{k}\cdot\boldsymbol{p}$
perturbation theory. We prove that the appearance of a $K$ dependent exchange
interaction is inseparably connected with a $K$ independent exchange
interaction of $P$ and $D$ excitons. We estimate the magnitude of these terms
for $\mathrm{Cu_{2}O}$ from microscopic calculations and show that they are far
too small to explain the observed $K$ dependent splitting. Instead, this
splitting has to be treated in terms of the dispersion of the excitons.
Furthermore, we prove the occurence of a coupling between longitudinal and
transverse excitons in $\mathrm{Cu_{2}O}$ due to the $K$ dependent nonanalytic
exchange interaction.

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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: math
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: stat