Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric Phase Effects in the Ultracold D + HD $\to$ D + HD and D + HD
  $\leftrightarrow$ H + D$_2$ Reactions   The results of accurate quantum reactive scattering calculations for the D +
HD($v=4$, $j=0$) $\to$ D + HD($v'$, $j'$), D + HD($v=4$, $j=0$) $\to$ H +
D$_2$($v'$, $j'$) and H + D$_2$($v=4$, $j=0$) $\to$ D + HD($v'$,$j'$) reactions
are presented for collision energies between $1\,\mu{\rm K}$ and $100\,{\rm
K}$. The ${\it ab\ initio}$ BKMP2 PES for the ground electronic state of H$_3$
is used and all values of total angular momentum between $J=0-4$ are included.
The general vector potential approach is used to include the geometric phase.
The rotationally resolved, vibrationally resolved, and total reaction rate
coefficients are reported as a function of collision energy. Rotationally
resolved differential cross sections are also reported as a function of
collision energy and scattering angle. Large geometric phase effects appear in
the ultracold reaction rate coefficients which result in a significant
enhancement or suppression of the rate coefficient (up to $3$ orders of
magnitude) relative to calculations which ignore the geometric phase. The
results are interpreted using a new quantum interference mechanism which is
unique to ultracold collisions. Significant effects of the geometric phase also
appear in the rotationally resolved differential cross sections which lead to a
very different oscillatory structure in both energy and scattering angle.
Several shape resonances occur in the $1$ - $10\,{\rm K}$ energy range and the
geometric phase is shown to significantly alter the predicted resonance
spectrum. The geometric phase effects depend sensitively on the nuclear spin
which may provide experimentalists with the ability to control the reaction by
the selection of a particular nuclear spin state.

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The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
2
The categories of this paper are: math
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an