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- W3099808789 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 $frac{a}{2} N^2 , omega^d$, where $N$ is the number of particles, $omega$ - 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 our 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 $a=-a_{F}<0$ is thermodynamically equivalent to the gas of repulsive bosons with $a=a_{B}>0$ provided the parameters $a_{F}$ and $a_{B}$ fulfill the relation $a_{B}+a_{F}=hbar$. This result supplements similar recent conclusion about thermodynamic equivalence of two-dimensional uniform imperfect repulsive Bose and attractive Fermi gases." @default.
- W3099808789 created "2020-11-23" @default.
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- W3099808789 date "2019-06-13" @default.
- W3099808789 modified "2023-10-18" @default.
- W3099808789 title "Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps" @default.
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- W3099808789 doi "https://doi.org/10.1088/1742-5468/ab190d" @default.
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