Quantum gas-liquid condensation in an attractive Bose gas

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.Comment: 12 pages, 8 figure

Meissner effect in a charged Bose gas with short-range repulsion

The question of whether the BEC is a necessary condition of the Meissner effect is examined. The electromagnetic susceptibility of a charged Bose gas with short-range repulsion is studied using the perturbation theory with respect to the repulsive force. With decreasing temperature, the Bose-statistical coherence grows, and prior to the BEC phase the susceptibility shows a singularity implying the Meissner effect. This means that the BEC is a sufficient, but not a necessary condition of the Meissner effect in the charged Bose gas with short-range repulsion.Comment: 8 pages, 3 figure

Nonclassical rotational behavior at the vicinity of the lamda point

The rotational property of a quantum liquid at the vicinity of the lambda point is examined. In a liquid helium 4 just above the lambda point, under the strong influence of Bose statistics, the coherent many-body wave function grows to an intermediate size between a macroscopic and a microscopic one, which is of a different nature from the thermal fluctuations. It must reflect in the rotational properties such as the moment of inertia. Beginning with the bosons without the condensate, we make a perturbation calculation of its susceptibility with respect to the repulsive interaction, and examine how, with decreasing temperature, the growth of the coherent wave function gradually changes the rotational behavior of a liquid:The moment of inertia slightly decreases just above the lambda point. This means that at the vicinity of the lambda point, the mechanical superfluid density does not always agree with the thermodynamical one.We compare the result to the experiment by Hess and Fairbank. A new interpretation of the shear viscosity just above the lambda point is given from this viewpoint.Comment: 12pages, 5figure