Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum N-Boson States and Quantized Motion of Solitonic Droplets:
  Universal Scaling Properties in Low Dimensions   In this article, we illustrate the scaling properties of a family of
solutions for N attractive bosonic atoms in the limit of large $N$. These
solutions represent the quantized dynamics of solitonic degrees of freedom in
atomic droplets. In dimensions lower than two, or $d=2-\epsilon$, we
demonstrate that the number of isotropic droplet states scales as
$N^{3/2}/\epsilon^{1/2}$, and for $\epsilon=0$, or $d=2$, scales as ${N^2}$.
The ground state energies scale as $N^{2 / \epsilon + 1}$ in $d=2-\epsilon$,
and when $d=2$, scale as an exponential function of N. We obtain the universal
energy spectra and the generalized Tjon relation; their scaling properties are
uniquely determined by the asymptotic freedom of quantum bosonic fields at
short distances, a distinct feature in low dimensions. We also investigate the
effect of quantum loop corrections that arise from various virtual processes
and show that the resultant lifetime for a wide range of excited states scales
as $N^{\epsilon/2}E^{1-\epsilon/2}$.

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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
2
The categories of this paper are: math
28
The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: eess
7
The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin