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Journal of the Physical Society of Japan

Dilute Bose System of Hard Spheres

Kapil M. Khanna

Published Nov 1, 1969• 4 citations
Publisher

Abstract

A realistic calculation of the normal-superfluid phase transition temperature of a dilute Bose system of hard spheres is presented. From the finiteness of the transition temperature it is concluded that such an assembly will be stable assembly.
DOI
10.1143/jpsj.27.1093

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arXiv:1004.0304•Apr 2, 2010•0 citations
By a generalization of the method used in a previous paper the distribution of energy levels of a dilute Bose system of hard spheres is found. These energy levels are then used to compute the statistical properties for the system. A phase transition is found, and the transition point is calculated to the lowest order of aaa, the diameter of the hard spheres. Furthermore, the thermodynamical functions of the system in both the gas phase and the degenerate phase are obtained, provided $(\frac{a}{\ensuremath{\lambda}})\ensuremath{\ll}1$ and $\ensuremath{\rho}{a}^{3}\ensuremath{\ll}1$, where $\ensuremath{\lambda}$ is the thermal wavelength and $\ensuremath{\rho}$ is the particle density.
We obtain thermodynamical functions for a dilute Bose gas of hard spheres by using the efffective Hamiltonian which is obtained by a quasi-linear transformation proposed previously and may be recognized as an improvement of the model Hamiltonian of Lee and Yang which is not correct about the terms of second order in the diameter of hard spheres when it is applied to the problem of the phase transition. The Bose condensation occurs at a temperature below which the degenerate phase of the quasi-particles appears. We evaluate the amount of the gap of the specific heat and that of the compressibility at the transition point.
We consider a dilute hard-sphere Bose gas in random external potentials at low temperatures, in D=3, using the technique of pseudopotentials and the Bogoliubov transformation. At absolute zero, the random potentials can deplete the Bose condensate, though not completely. On the other hand, they generate an amount of normal fluid equal to 4/3 the condensate depletion. This is a localization effect that can destroy superfluidity at absolute zero. General features of the superfluid density in the neighborhood of this transition point agree qualitatively with experimental results on helium in porous media.
The phase transitions at finite temperatures in the systems described by the Bose-Fermi-Hubbard model are investigated in this work in the framework of the selfconsistent random phase approximation. The case of the hard-core bosons is considered and pseudospin formalism is used. The density-density correlator is calculated in the random phase approximation and the possibilities of transitions from superfluid to supersolid phases are investigated. It is shown that the transitions between uniform and charge ordered phases can be of the second or the first order, depending on the system parameters.