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arXiv:0903.0260 · Physical Review A

Nonperturbative thermodynamics of an interacting Bose gas

Stefan Floerchinger, CHRISTOF WETTERICH

Published Jun 1, 2009• 25 citations
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Abstract

We discuss the thermodynamics of a nonrelativistic gas of bosons with a local repulsive interaction. In particular, we compute the temperature and density dependences of pressure, energy and entropy densities, superfluid and condensate fractions, correlation length, specific heat, isothermal and adiabatic compressibilities, and various sound velocities. The $T\ensuremath{\rightarrow}0$ limit approaches the quantum phase transition, while the universal critical behavior of a classical second-order phase transition in the O(2) universality class determines the region around the critical temperature. Our nonperturbative flow equations based on exact functional renormalization cover all regions in the phase diagram.

DOI
10.1103/physreva.79.063602

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We discuss the thermodynamics of a nonrelativistic gas of bosons with a local repulsive interaction. In particular, we compute the temperature and density dependences of pressure, energy and entropy densities, superfluid and condensate fractions, correlation length, specific heat, isothermal and adiabatic compressibilities, and various sound velocities. The T\ensuremath→0T\ensuremath{\rightarrow}0T\ensuremath→0 limit approaches the quantum phase transition, while the universal critical behavior of a classical second-order phase transition in the O(2) universality class determines the region around the critical temperature. Our nonperturbative flow equations based on exact functional renormalization cover all regions in the phase diagram.
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.
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The critical properties of the phase transition from a normal gas to a BEC (superfluid) of a harmonically confined Bose gas are analyzed using a proposed model for the equation of state of the underlying homogenous Bose fluid. The equation of state is given in terms of the homogenous particle density as a function of the chemical potential and temperature of the gas. On the normal side of the fluid it is assumed to be an ideal Bose gas while in the superfluid state we propose a function 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 {\it global} thermodynamics of the harmonically confined gas which shows that, at the critical transition of the confined gas, the thermodynamic susceptibilities, such as the isothermal compressibility, do not diverge, in contrast to the behavior of the uniform gas. The singularity of the critical transition in the confined system appears now at the derivatives of the susceptibilities. We discuss how these properties can be experimentally tested.
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