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 , where N is the number of particles, —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 is thermodynamically equivalent to the gas of repulsive bosons with provided the parameters and fulfill the relation . This result supplements similar recent conclusion about thermodynamic equivalence of two-dimensional (2D) uniform imperfect repulsive Bose and attractive Fermi gases.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 , where N is the number of particles, —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 is thermodynamically equivalent to the gas of repulsive bosons with provided the parameters and fulfill the relation . This result supplements similar recent conclusion about thermodynamic equivalence of two-dimensional (2D) uniform imperfect repulsive Bose and attractive Fermi gases.

arXiv:1810.02209Journal of Statistical Mechanics Theory and ExperimentJun 1, 20196 citations

Thermodynamics of a one-dimensional Bose gas with repulsive contact interactions

Giulia De Rosi, Pietro Massignan, Maciej Lewenstein +1 more

May 17, 20190 citations

Dilute bose gas in a quasi two-dimensional trap

Brandon P. van Zyl, R. K. Bhaduri, Justin Sigetich

We investigate the behavior of a dilute quasi two-dimensional, harmonically confined, weakly interacting Bose gas within the finite-temperature Thomas-Fermi approximation. We find that the thermodynamic properties of the system are markedly different for repulsive and attractive interactions. Specifically, in contrast to the repulsive case, there appears to be a phase transition when the atoms interact with an attractive pseudo-potential, in the sense that there is no self-consistent solution for the normal ground state below a certain temperature $T^{\star}$ . These numerical findings are supported by analytical investigations of the thermodynamics of the system in the complex fugacity plane, and within the random-phase approximation. We also show that the temperature $T^{\star}$ can be interpreted as the limiting temperature below which the system cannot be described as a collection of noninteracting {\em haldons}.We investigate the behavior of a dilute quasi two-dimensional, harmonically confined, weakly interacting Bose gas within the finite-temperature Thomas-Fermi approximation. We find that the thermodynamic properties of the system are markedly different for repulsive and attractive interactions. Specifically, in contrast to the repulsive case, there appears to be a phase transition when the atoms interact with an attractive pseudo-potential, in the sense that there is no self-consistent solution for the normal ground state below a certain temperature $T^{\star}$. These numerical findings are supported by analytical investigations of the thermodynamics of the system in the complex fugacity plane, and within the random-phase approximation. We also show that the temperature $T^{\star}$ can be interpreted as the limiting temperature below which the system cannot be described as a collection of noninteracting {\em haldons}.

arXiv:cond-mat/0106410Journal of Physics B Atomic Molecular and Optical PhysicsJun 20, 200111 citations

Thermodynamics of a Trapped Bose-Condensed Gas

S. Giorgini, Лев П. Питаевский, S. Stringari

arXiv:cond-mat/9704014Journal of Low Temperature PhysicsOct 1, 1997185 citations

Thermodynamic equivalence of two-dimensional imperfect attractive Fermi and repulsive Bose gases

Marek Napiórkowski, J. Piasecki

We consider two-dimensional imperfect attractive Fermi and repulsive Bose gases consisting of spinless point particles whose total interparticle interaction energy is represented by $a{N}^{2}/2V$ with $a=\ensuremath{-}{a}_{F}\ensuremath{\le}0$ for fermions and $a={a}_{B}\ensuremath{\ge}0$ for bosons. We show that, in spite of the attraction, the thermodynamics of a $d=2$ imperfect Fermi gas remains well defined for $0\ensuremath{\le}{a}_{F}\ensuremath{\le}{a}_{0}={h}^{2}/2\ensuremath{\pi}m$, and is exactly the same as the one of the repulsive imperfect Bose gas with ${a}_{B}={a}_{0}\ensuremath{-}{a}_{F}$. In particular, for ${a}_{F}={a}_{0}$ one observes the thermodynamic equivalence of the attractive imperfect Fermi gas and the ideal Bose gas.We consider two-dimensional imperfect attractive Fermi and repulsive Bose gases consisting of spinless point particles whose total interparticle interaction energy is represented by $a{N}^{2}/2V$ with $a=\ensuremath{-}{a}_{F}\ensuremath{\le}0$ for fermions and $a={a}_{B}\ensuremath{\ge}0$ for bosons. We show that, in spite of the attraction, the thermodynamics of a $d=2$ imperfect Fermi gas remains well defined for $0\ensuremath{\le}{a}_{F}\ensuremath{\le}{a}_{0}={h}^{2}/2\ensuremath{\pi}m$, and is exactly the same as the one of the repulsive imperfect Bose gas with ${a}_{B}={a}_{0}\ensuremath{-}{a}_{F}$. In particular, for ${a}_{F}={a}_{0}$ one observes the thermodynamic equivalence of the attractive imperfect Fermi gas and the ideal Bose gas.

arXiv:1705.09511Physical Review AJun 29, 20179 citations

Thermodynamic properties of a trapped interacting Bose gas

Hualin Shi, Wei‐Mou Zheng

arXiv:cond-mat/9611171Physica A Statistical Mechanics and its ApplicationsSep 1, 199810 citations

T^{\star}

. These numerical findings are supported by analytical investigations of the thermodynamics of the system in the complex fugacity plane, and within the random-phase approximation. We also show that the temperature

T^{\star}

can be interpreted as the limiting temperature below which the system cannot be described as a collection of noninteracting {\em haldons}.

We consider two-dimensional imperfect attractive Fermi and repulsive Bose gases consisting of spinless point particles whose total interparticle interaction energy is represented by

a{N}^{2}/2V

with $a=\ensuremath{-}{a}_{F}\ensuremath{\le}0$ for fermions and $a={a}_{B}\ensuremath{\ge}0$ for bosons. We show that, in spite of the attraction, the thermodynamics of a

d=2

imperfect Fermi gas remains well defined for $0\ensuremath{\le}{a}_{F}\ensuremath{\le}{a}_{0}={h}^{2}/2\ensuremath{\pi}m$, and is exactly the same as the one of the repulsive imperfect Bose gas with ${a}_{B}={a}_{0}\ensuremath{-}{a}_{F}$. In particular, for

{a}_{F}={a}_{0}

one observes the thermodynamic equivalence of the attractive imperfect Fermi gas and the ideal Bose gas.