Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Low-lying energy levels of a one-dimensional weakly interacting Bose gas
  under zero boundary conditions   We diagonalize the second-quantized Hamiltonian of a one-dimensional Bose gas
with a nonpoint repulsive interatomic potential and zero boundary conditions.
At weak coupling the solutions for the ground-state energy $E_{0}$ and the
dispersion law $E(k)$ coincide with the Bogoliubov solutions for a periodic
system. In this case, the single-particle density matrix $F_{1}(x,x^{\prime})$
at $T=0$ is close to the solution for a periodic system and, at $T>0$, is
significantly different from it. We also obtain that the wave function $\langle
\hat{\psi}(x,t) \rangle$ of the effective condensate is close to a constant
$\sqrt{N_{0}/L}$ inside the system and vanishes on the boundaries (here,
$N_{0}$ is the number of atoms in the effective condensate, and $L$ is the size
of the system). We find the criterion of applicability of the method, according
to which the method works for a finite system at very low temperature and with
a weak coupling (a weak interaction or a large concentration).

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The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an