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arXiv:2011.05628 · Physica Scripta

Thermodynamics of a weakly interacting Bose gas above the transition temperature

M S Bulakhov, A S Peletminskii, Yu V Slyusarenko, A G Sotnikov

Published Jan 18, 2021• 2 citations
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Abstract

Abstract We study thermodynamic properties of weakly interacting Bose gases above the transition temperature of Bose–Einstein condensation in the framework of a thermodynamic perturbation theory. Cases of local and non-local interactions between particles are analyzed both analytically and numerically. We obtain and compare the temperature dependencies for the chemical potential, entropy, pressure, and specific heat to those of noninteracting gases. The results set reliable benchmarks for thermodynamic characteristics and their asymptotic behavior in dilute atomic and molecular Bose gases above the transition temperature.

DOI
10.1088/1402-4896/abdcf5

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Abstract We study thermodynamic properties of weakly interacting Bose gases above the transition temperature of Bose–Einstein condensation in the framework of a thermodynamic perturbation theory. Cases of local and non-local interactions between particles are analyzed both analytically and numerically. We obtain and compare the temperature dependencies for the chemical potential, entropy, pressure, and specific heat to those of noninteracting gases. The results set reliable benchmarks for thermodynamic characteristics and their asymptotic behavior in dilute atomic and molecular Bose gases above the transition temperature.
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We present a systematic study of dilute three-dimensional dipolar Bose gas employing a finite temperature perturbation theory (beyond the mean field). We analyze in particular the behavior of the anomalous density, we find that this quantity has a finite value in the limit of weak interactions at both zero and finite temperatures. We show that the presence of the dipole–dipole interaction enhances fluctuations, the second order correlation function and thermodynamic quantities such as the chemical potential, the ground state energy, the compressibility and the superfluid fraction. We identify the validity criterion of the small parameter of the theory for Bose-condensed dipolar gases.
Abstract The critical properties of the phase transition from a normal gas to a Bose–Einstein condensate (superfluid) of a harmonically confined Bose gas are addressed with the knowledge of an equation of state of the underlying homogeneous Bose fluid. It is shown that while the presence of the confinement trap arrests the usual divergences of the isothermal compressibility and heat capacities, the critical behavior manifests itself now in the divergence of derivatives of the mentioned susceptibilities. This result is illustrated with a mean-field like model of an equation of state for the homogeneous particle density as a function of the chemical potential and temperature of the gas. The model assumes the form of an ideal Bose gas in the normal fluid while in the superfluid state a function is proposed such that, both, asymptotically reaches the Thomas–Fermi solution of a weakly interacting Bose gas at large densities and low temperatures and, at the transition, matches the critical properties of the ideal Bose gas. With this model we obtain the global thermodynamics of the harmonically confined gas, from which we analyze its critical properties. We discuss how these properties can be experimentally tested.
We study the condensation of a homogeneous interacting Bose gas in the presence of a superimposed weak periodic potential. In contrast to, e.g., a harmonic trap, the periodic potential does not reduce the significance of long-wavelength fluctuations and thus influences the phase transition in a more profound way. We present general thermodynamic descriptions of the system above condensation in terms of mean-field as well as renormalization-group theory. Our approaches are based on describing the interplay between the effects of the interactions and the potential by means of a renormalization of the potential amplitude. These theories are then used to study the critical chemical potential and particle density and their dependence on the properties of the applied potential. A main result of our investigations concerns the characteristic nonperturbative momentum scale kc{k}_{c}kc​ of the critical interacting Bose gas. It is shown that the existence of this momentum scale becomes macroscopically manifest in the behavior of the critical thermodynamic properties.
The thermodynamic properties and finite-size scaling of weakly interacting Bose gases with a finite number of particles confined in a cubic box of volume L3{L}^{3}L3 with periodic boundary conditions are investigated theoretically based on an exact recursion relation for the canonical-ensemble partition function. In a similar manner to the case of an ideal Bose gas, the recursive scheme of the interacting finite system at any temperatures is established in the framework of the Bogoliubov theory. The temperature dependence of the condensate fraction and specific heat with different particles and interactions is obtained numerically. By defining two different transition temperatures of the finite systems, the effect of interactions on the transition temperatures yields the different and nonmonotonous behaviors. The finite-size scaling condensate fraction at the transition temperature for the systems is also discussed. It is shown that the calculated finite-size scaling is universally independent on the various system sizes and transition temperatures.
We present precise path-integral Monte Carlo results for the thermodynamics of a homogeneous dilute Bose gas. Pressure and energy are calculated as a function of temperature both below and above the Bose-Einstein transition. Specifically, we address interaction effects, focusing on deviations from the ideal-gas law in the thermodynamic limit. We also calculate the isothermal compressibility and the contact parameter, which provide a clear signature of the role played by interactions. In particular, we obtain indications of a discontinuity of the compressibility at the transition point. To gain physical insight, numerical results are systematically compared with the predictions of first-order Hartree-Fock and second-order Popov theories, both giving an approximate description of the gas thermodynamics. The comparison shows the extension of the critical region around the transition point, where the inaccuracies of the perturbative expansions are more pronounced.