Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the role of hyperfine-interactions-mediated Zeeman effect in the
  condensation temperature shift of trapped atomic Bose-Einstein condensates   We discuss the effect of interatomic interactions on the condensation
temperature $T_c$ of a laboratory atomic Bose-Einstein condensate under the
influence of an external trapping magnetic field. We predict that accounting
for hyperfine interactions mediated Zeeman term in the mean-field approximation
produces, in the case of the $403 \, G$ Feshbach resonance in the $|F,m_F> =
|1,1>$ hyperfine state of a $^{39}K$ condensate, with $F$ the total spin of the
atom, an experimentally observed (and not yet explained) shift in the
condensation temperature $\Delta T_{c}/T_{c}^{0}=b^{*}_0+b^{*}_1
(a/\lambda_{T}) + b^{*}_2 (a/\lambda_{T})^2$ with $b^{*}_0 \simeq 0.0002$,
$b^{*}_1 \simeq -3.4$ and $b^{*}_2 \simeq 47$, where $a$ is the s-wave
scattering length, and $\lambda_T$ is the thermal wavelength at $T_{c}^{0}$.
Generic expressions for the coefficients $b^*_0$, $b^*_1$ and $b^*_2$ are also
obtained, which can be used to predict the temperature shift for other Feshbach
resonances of $^{39}K$ or other atomic condensates.

28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg