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Physical Review

Superfluidity of an Ideal Bose-Einstein Gas

John M. Blatt, S. T. Butler

Published Oct 15, 1955• 55 citations
Publisher

Abstract

An equilibrium superfluid is defined as a substance whose moment of inertia in thermal equilibrium is less than the classical value. The ideal Bose-Einstein gas below its transition temperature is shown to be an equilibrium superfluid. However, a more detailed analysis of the relation between angular momentum and angular velocity shows that experiments carried out with practical angular momenta and velocities would give an abnormally large apparent moment of inertia in thermal equilibrium, i.e., the gas would appear to be an "infrafluid." Nevertheless, a weakly interacting Bose-Einstein gas can be used as a model of a superfluid, if the superfluid state is assumed to be metastable rather than the thermodynamic equilibrium state.

DOI
10.1103/physrev.100.476

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An equilibrium superfluid is defined as a substance whose moment of inertia in thermal equilibrium is less than the classical value. The ideal Bose-Einstein gas below its transition temperature is shown to be an equilibrium superfluid. However, a more detailed analysis of the relation between angular momentum and angular velocity shows that experiments carried out with practical angular momenta and velocities would give an abnormally large apparent moment of inertia in thermal equilibrium, i.e., the gas would appear to be an "infrafluid." Nevertheless, a weakly interacting Bose-Einstein gas can be used as a model of a superfluid, if the superfluid state is assumed to be metastable rather than the thermodynamic equilibrium state.
Abstract The explanation of the phenomenon of superfluidity requires an in‐depth analysis of both equilibrium and nonequilibrium statistics. This can be done in dilute gases by a systematic expansion in powers of the density, as done for classical gases in Prigogine's book on kinetic theory. Following the method of expansion of Prigogine and Résibois, the thermodynamics of a dilute gas of N identical Bosons with condensate can be studied in the case of a superflow, that is, of a finite and uniform velocity difference between the normal and superfluid component (assumed at rest). The microscopic interactions between the two components conserve the momentum of the normal component, making it a thermodynamic parameter. No thermal equilibrium exists if the velocity difference is larger than a critical value far below the onset of dissipation given by Landau's criterion. Consequences of this are discussed. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004
In a dilute Bose gas the interaction between the normal gas and the condensate can be studied both at equilibrium and for its relevance to superfluid mechanics. In this article, one reviews first the thermodynamics of the interacting Bose gas in the low density limit and in the low temperature–finite density case. This is extended to thermodynamics with a velocity difference between the two components, normal and superfluid. It is argued that, if the initial value of the momentum related to this velocity difference is larger than the one given by thermodynamic stability, a new condensate should form in a finite time with a velocity close to the that of the normal gas. In the dilute case this occurrence of a new condensate is reminiscent of the condensation in the isotropic case at high enough density.
We have investigated the superfluid properties of a ring of weakly interacting and degenerate 1D Bose gas at thermal equilibrium with a rotating vessel. The conventional definition of superfluidity predicts that the gas has a significant superfluid fraction only in the Bose condensed regime. In the opposite regime, it is found that a superfluid behaviour can still be identified when the probability distribution of the total momentum of the gas has a multi-peaked structure, revealing unambiguously the existence of ‘superfluid’ supercurrent states that did not show up in the conventional definition of superfluidity.