Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Second-order flows for computing the ground states of rotating
  Bose-Einstein condensates   Second-order flows in this paper refer to some artificial evolutionary
differential equations involving second-order time derivatives distinguished
from gradient flows which are considered to be first-order flows. This is a
popular topic due to the recent advances of inertial dynamics with damping in
convex optimization. Mathematically, the ground state of a rotating
Bose-Einstein condensate (BEC) can be modelled as a minimizer of the
Gross-Pitaevskii energy functional with angular momentum rotational term under
the normalization constraint. We introduce two types of second-order flows as
energy minimization strategies for this constrained non-convex optimization
problem, in order to approach the ground state. The proposed artificial
dynamics are novel second-order nonlinear hyperbolic partial differential
equations with dissipation. Several numerical discretization schemes are
discussed, including explicit and semi-implicit methods for temporal
discretization, combined with a Fourier pseudospectral method for spatial
discretization. These provide us a series of efficient and robust algorithms
for computing the ground states of rotating BECs. Particularly, the newly
developed algorithms turn out to be superior to the state-of-the-art numerical
methods based on the gradient flow. This is judged by the fact that larger size
of time steps can be applied in explicit methods, and much smaller number of
time steps are needed in both explicit and semi-implicit discretizations, while
every time step encounters almost the same computational complexity in
comparison with the respective gradient flow type approaches. Rich and detailed
numerical examples are documented for verification and comparison.

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The categories of this paper are: chem-ph
3
The categories of this paper are: physics
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The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con