Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local density approximation for a perturbative equation of state   The knowledge of a series expansion of the equation of state provides a deep
insight into the physical nature of a quantum system. Starting from a generic
``perturbative'' equation of state of a homogeneous ultracold gas we make
predictions for the properties of the gas in the presence of harmonic
confinement. The local density approximation is used to obtain the chemical
potential, total and release energies, Thomas-Fermi size and density profile of
a trapped system in three-, two-, and one- dimensional geometries. The
frequencies of the lowest breathing modes are calculated using scaling and
sum-rule approaches and could be used in an experiment as a high precision tool
for obtaining the expansion terms of the equation of state. The derived
formalism is applied to dilute Bose and Fermi gases in different dimensions and
to integrable one-dimensional models. Physical meaning of expansion terms in a
number of systems is discussed.

29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph