@article{6840,
  abstract     = {We discuss thermodynamic properties of harmonically trapped
imperfect quantum gases. The spatial inhomogeneity of these systems imposes
a redefinition of the mean-field interparticle potential energy as compared
to the homogeneous case. In our approach, it takes the form a
2N2 ωd, where
N is the number of particles, ω—the harmonic trap frequency, d—system’s
dimensionality, and a is a parameter characterizing the interparticle interaction.
We provide arguments that this model corresponds to the limiting case of
a long-ranged interparticle potential of vanishingly small amplitude. This
conclusion is drawn from a computation similar to the well-known Kac scaling
procedure, which is presented here in a form adapted to the case of an isotropic
harmonic trap. We show that within the model, the imperfect gas of trapped
repulsive bosons undergoes the Bose–Einstein condensation provided d > 1.
The main result of our analysis is that in d = 1 the gas of attractive imperfect
fermions with a = −aF < 0 is thermodynamically equivalent to the gas of
repulsive bosons with a = aB > 0 provided the parameters aF and aB fulfill
the relation aB + aF = . This result supplements similar recent conclusion
about thermodynamic equivalence of two-dimensional (2D) uniform imperfect
repulsive Bose and attractive Fermi gases.},
  author       = {Mysliwy, Krzysztof and Napiórkowski, Marek},
  issn         = {1742-5468},
  journal      = {Journal of Statistical Mechanics: Theory and Experiment},
  number       = {6},
  publisher    = {IOP Publishing},
  title        = {{Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps}},
  doi          = {10.1088/1742-5468/ab190d},
  volume       = {2019},
  year         = {2019},
}