Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Particle-Number-Conserving Bogoliubov Approximation for Bose-Einstein
  Condensates Using Extended Catalytic States   We encode the many-body wavefunction of a Bose-Einstein condensate (BEC) in
the $N$-particle sector of an extended catalytic state. This catalytic state is
a coherent state for the condensate mode and an arbitrary state for the modes
orthogonal to the condensate mode. Going to a time-dependent interaction
picture where the state of the condensate mode is displaced to the vacuum, we
can organize the effective Hamiltonian by powers of ${N}^{-1/2}$. Requiring the
terms of order ${N}^{1/2}$ to vanish gives the Gross-Pitaevskii equation. Going
to the next order, $N^0$, we derive equations for the number-conserving
Bogoliubov approximation, first given by Castin and Dum [Phys. Rev. A
$\textbf{57}$, 3008 (1998)]. In contrast to other approaches, ours is well
suited to calculating the state evolution in the Schr\"{o}dinger picture;
moreover, it is straightforward to generalize our method to multi-component
BECs and to higher-order corrections.

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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: math
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The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio