Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum dark solitons in the 1D Bose gas: From single to double
  dark-solitons   We study quantum double dark-solitons by constructing corresponding quantum
states in the Lieb-Liniger model for the one-dimensional Bose gas. Here we
expect that the Gross-Pitaevskii (GP) equation should play a central role in
the long distance mean-field behavior of the 1D Bose gas. We first introduce
novel quantum states of a single dark soliton with a nonzero winding number. We
show them by exactly evaluating not only the density profile but also the
profiles of the square amplitude and phase of the matrix element of the field
operator between the $N$-particle and $(N-1)$-particle states. For elliptic
double dark-solitons, the density and phase profiles of the corresponding
states almost perfectly agree with those of the classical solutions,
respectively, in the weak coupling regime. We then show that the scheme of the
mean-field product state is quite effective for the quantum states of double
dark solitons. Assigning the ideal Gaussian weights to a sum of the excited
states with two particle-hole excitations we obtain double dark-solitons of
distinct narrow notches with different depths. We suggest that the mean-field
product state should be well approximated by the ideal Gaussian weighted sum of
the low excited states with a pair of particle-hole excitations. The results of
double dark-solitons should be fundamental and useful for constructing quantum
multiple dark-solitons.

3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg