Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nature of Lieb's "hole" excitations and two-phonon states of a Bose gas   It is generally accepted that the ``hole'' and ``particle'' excitations are
two independent types of excitations of a one-dimensional system of point
bosons. We show for a weak coupling that the Lieb's ``hole'' with the momentum
$p=j2\pi/L$ is $j$ identical interacting phonons with the momentum $2\pi/L$
(here, $L$ is the size of the system, and $\hbar=1$). We prove this assertion
for $j=1, 2$ by comparing solutions for a system of point bosons with solutions
for a system of nonpoint bosons obtained in the limit of the point interaction.
The additional arguments show that our conclusion should be true for any $j=1,
2, \ldots, N$. Thus, at a weak coupling, the holes are not a physically
independent type of quasiparticles. Moreover, we find the solution for two
interacting phonons in a Bose system with an interatomic potential of the
general form at a weak coupling and any dimension (1, 2, or 3). It is also
shown for a weak coupling that the largest number of phonons in a Bose system
is equal to the number of atoms $N$. Finally, we have studied the structure of
wave functions for the Tonks--Girardeau gas and found that the properties of
quasiparticles in this regime are quite strange.

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The categories of this paper are: stat
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The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph