Statistical mechanics of the gas–liquid condensation in the attractive Bose gas

Sangita Bera, M. L. Lekala, Barnali Chakrabarti +2 more

Randall G. Hulet

Shun-ichiro Koh

Gas-liquid condensation (GLC) in an attractive Bose gas is studied on the basis of statistical mechanics. Using some results in combinatorial mathematics, the following are derived. (1) With decreasing temperature, the Bose-statistical coherence grows in the many-body wave function, which gives rise to the divergence of the grand partition function prior to Bose-Einstein condensation. It is a quantum-mechanical analogue to the GLC in a classical gas (quantum GLC). (2) This GLC is triggered by the bosons with zero momentum. Compared with the classical GLC, an incomparably weaker attractive force creates it. For the system showing the quantum GLC, we discuss a cold helium 4 gas at sufficiently low pressure.

Shun-ichiro Koh

Gas-liquid condensation (GLC) in the attractive uniform Bose gas is studied by applying the idea of the Yang-Lee zeros to its grand partition function. The followings are proved: (i) When the temperature decreases and the density increases, the GLC occurs prior to the Bose-Einstein condensation (BEC), (ii) an explosive growth of the Bose-statistical coherence to a macroscopic scale occurs simultaneously with the GLC, which are triggered by bosons with a zero momentum, and (iii) the GLC in the Bose gas is not only a condensation in coordinate space, but also in momentum space. On the basis of these results, a comparative study of the BEC and the GLC is developed. Further, we discuss its implication to the trapped atomic gas.

Yu. Kagan, Boris V. Svistunov, Gora V. Shlyapnikov +1 more

Tobias Damm, Julian Schmitt, Qi Liang +4 more

Phase transitions, as the condensation of a gas to a liquid, are often revealed by a discontinuous behaviour of thermodynamic quantities. For liquid helium, for example, a divergence of the specific heat signals the transition from the normal fluid to the superfluid state. Apart from liquid helium, determining the specific heat of a Bose gas has proven to be a challenging task, for example, for ultracold atomic Bose gases. Here we examine the thermodynamic behaviour of a trapped two-dimensional photon gas, a system that allows us to spectroscopically determine the specific heat and the entropy of a nearly ideal Bose gas from the classical high temperature to the Bose-condensed quantum regime. The critical behaviour at the phase transition is clearly revealed by a cusp singularity of the specific heat. Regarded as a test of quantum statistical mechanics, our results demonstrate a quantitative agreement with its predictions at the microscopic level.