Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Inhomogeneous Gaussian Free Field, with application to ground state
  correlations of trapped 1d Bose gases   Motivated by the calculation of correlation functions in inhomogeneous
one-dimensional (1d) quantum systems, the 2d Inhomogeneous Gaussian Free Field
(IGFF) is studied and solved. The IGFF is defined in a domain $\Omega \subset
\mathbb{R}^2$ equipped with a conformal class of metrics $[{\rm g}]$ and with a
real positive coupling constant $K: \Omega \rightarrow \mathbb{R}_{>0}$ by the
action $\mathcal{S}[h] = \frac{1}{8\pi } \int_\Omega \frac{\sqrt{{\rm g}} d^2
{\rm x}}{K({\rm x})} \, {\rm g}^{i j} (\partial_i h)(\partial_j h)$. All
correlations functions of the IGFF are expressible in terms of the Green's
functions of generalized Poisson operators that are familiar from 2d
electrostatics in media with spatially varying dielectric constants.
  This formalism is then applied to the study of ground state correlations of
the Lieb-Liniger gas trapped in an external potential $V(x)$. Relations with
previous works on inhomogeneous Luttinger liquids are discussed. The main
innovation here is in the identification of local observables $\hat{O} (x)$ in
the microscopic model with their field theory counterparts $\partial_x h, e^{i
h(x)}, e^{-i h(x)}$, etc., which involve non-universal coefficients that
themselves depend on position --- a fact that, to the best of our knowledge,
was overlooked in previous works on correlation functions of inhomogeneous
Luttinger liquids ---, and that can be calculated thanks to Bethe Ansatz form
factors formulae available for the homogeneous Lieb-Liniger model. Combining
those position-dependent coefficients with the correlation functions of the
IGFF, ground state correlation functions of the trapped gas are obtained.
Numerical checks from DMRG are provided for density-density correlations and
for the one-particle density matrix, showing excellent agreement.

3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs