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 $a$ , 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.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 $a$, 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.

Physical ReviewDec 1, 1958193 citations

Thermodynamics of Bose-condensed atomic hydrogen

Beatrice Pozzi, Luca Salasnich, Alberto Parola +1 more

arXiv:cond-mat/0004038The European Physical Journal DAug 1, 20002 citations

Bose–Einstein Condensation and Superfluidity

Kerson Huang

We review generally accepted definitions of Bose–Einstein condensation and superfluidity, emphasizing that they are independent concepts. These ideas are illustrated in a dilute hard-sphere Bose gas, which is relevant to experiments on excitons and spin-aligned atomic hydrogen. We then discuss superfluid He in porous media, as simulated by different models in different regimes. At low coverage, we model it by a dilute hard-sphere Bose gas in random potentials, and show that superfluidity is destroyed through the pinning of the Bose condensate by the external potentials. At full coverage, we model the random medium by an ohmic network of random resistors, and argue that the superfluid transition is a percolation transition in d = 3, with critical exponent 1.7. This book is devoted to the phenomenon of Bose–Einstein condensation [1, 2] and inevitably, its relevance to superfluidity [3]. To provide some background for other articles in this volume, I would like to summarize some commonly accepted views on these phenomena, and illustrate them in the context of a dilute hard-sphere Bose gas, a model in which we have some control over the approximations made. I will also describe some recent work on the effect of randomness on the Bose condensate, which shows that Bose–Einstein condensation does not automatically give rise to superfluidity.We review generally accepted definitions of Bose–Einstein condensation and superfluidity, emphasizing that they are independent concepts. These ideas are illustrated in a dilute hard-sphere Bose gas, which is relevant to experiments on excitons and spin-aligned atomic hydrogen. We then discuss superfluid He in porous media, as simulated by different models in different regimes. At low coverage, we model it by a dilute hard-sphere Bose gas in random potentials, and show that superfluidity is destroyed through the pinning of the Bose condensate by the external potentials. At full coverage, we model the random medium by an ohmic network of random resistors, and argue that the superfluid transition is a percolation transition in d = 3, with critical exponent 1.7. This book is devoted to the phenomenon of Bose–Einstein condensation [1, 2] and inevitably, its relevance to superfluidity [3]. To provide some background for other articles in this volume, I would like to summarize some commonly accepted views on these phenomena, and illustrate them in the context of a dilute hard-sphere Bose gas, a model in which we have some control over the approximations made. I will also describe some recent work on the effect of randomness on the Bose condensate, which shows that Bose–Einstein condensation does not automatically give rise to superfluidity.

Cambridge University Press eBooksApr 6, 199528 citations

a

, 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.