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Contemporary Physics

Quantum fluids

David S. Betts

Published May 1, 1969• 10 citations
Publisher

Abstract

A quantum fluid is one in which energy quantization has a marked effect on behaviour. Sometimes the effect can be dramatic, as with superfluid helium and with the electron gas in superconducting metals. In this article a simple criterion for distinguishing quantum fluids is obtained, and this is followed by a brief outline of the properties of perfect quantum gases. These ideas are then used as a unifying framework, within which some properties of real quantum fluids sre described and analysed. The approach to the subject is descriptive and physical, with very little dependence on mathematical argument.

DOI
10.1080/00107516908224595

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A quantum fluid is one in which energy quantization has a marked effect on behaviour. Sometimes the effect can be dramatic, as with superfluid helium and with the electron gas in superconducting metals. In this article a simple criterion for distinguishing quantum fluids is obtained, and this is followed by a brief outline of the properties of perfect quantum gases. These ideas are then used as a unifying framework, within which some properties of real quantum fluids sre described and analysed. The approach to the subject is descriptive and physical, with very little dependence on mathematical argument.
The term quantum turbulence denotes the turbulent motion of quantum fluids, systems such as superfluid helium and atomic Bose-Einstein condensates, which are characterized by quantized vorticity, superfluidity, and, at finite temperatures, two-fluid behavior. This article introduces their basic properties, describes types and regimes of turbulence that have been observed, and highlights similarities and differences between quantum turbulence and classical turbulence in ordinary fluids. Our aim is also to link together the articles of this special issue and to provide a perspective of the future development of a subject that contains aspects of fluid mechanics, atomic physics, condensed matter, and low-temperature physics.
The phenomena of superfluidity and superconductivity are intimately connected with the existence of a condensate, a macroscopically occupied quantum state. Such condensates occur in a variety of different physical systems, as described in Chapter 1. The foundation for the description of superfluidity is a picture of the system as being comprised of a condensate and elementary excitations. In Chapter 8 we have seen how physical properties such as the energy and the density of a Bose–Einstein condensed system may be expressed in terms of a contribution from the condensate, plus one from the elementary excitations, and in this chapter we shall consider further developments of this basic idea to other situations. As a first application, we determine the critical velocity for creation of an excitation in a homogeneous system (Sec. 10.1). Following that, we show how to express the momentum density in terms of the velocity of the condensate and the distribution function for excitations. This provides the basis for a two-component description, the two components being the condensate and the thermal excitations (Sec. 10.2). In the past, this framework has proved to be very effective in describing the properties of superfluids and superconductors, and in Sec. 10.3 we apply it to dynamical processes. To describe the state of a superfluid, one must specify the condensate velocity, in addition to the variables needed to characterize the state of an ordinary fluid. As a consequence, the collective behaviour of a superfluid is richer than that of an ordinary one. Collective modes are most simply examined when excitations collide frequently enough that they are in local thermodynamic equilibrium.
When liquid helium-4 is cooled to 2.17 K it changes from an ordinary fluid to a superfluid somewhat similar in nature to superfluid helium-3 and to the electron fluid in superconductors. Extensive investigation over the last five decades has given us a highly refined phenomenological description of how superfluid He4 behaves, even though the underlying quantum theory is only partially understood. Much of the current research on superfluid He4 is part of a continuing effort to work out the implications of this phenomenological description, in the same way as classical fluid dynamicists are still working out the implications of the Navier-Stokes equations.
We discuss the generic phase diagrams of pure systems that remain fluid near zero temperature. We call this phase a quantum fluid. We argue that the signature of the transition is the change of sign of the chemical potential, being negative in the normal phase and becoming positive in the quantum fluid phase. We show that this change is characterized by a phenomenon that we call condensation, in which a macroscopic number of particles is in their own many-body ground state, a situation common to Fermi and Bose gases. We show that the ideal Bose-Einstein Condensation fits in this scenario, but that it also permits the occurrence of a situation that we may call "Fermi-Dirac Condensation". In addition, we argue that this phenomenon is also behind the development of superfluid phases in real interacting fluids. However, only interacting systems may show the change from a thermal fluid to a quantum one as a true phase transition. As a corollary, this argument shows the necessity of the appearance of a "supersolid" phase. We also indicate how these ideas may be useful in the description of of experiments with ultracold alkali gases.
In January 1938, the Russian physicist Pyotr Kapitza reported that, at temperatures below 2.2 degrees above absolute zero, liquid helium seemed to flow with no loss of energy due to friction. The term “superfluid” was suggested to describe this new behavior—which was eventually understood as a dramatic illustration of the quantum-mechanical wave nature of matter. The study of such macroscopic quantum effects now lies at the heart of modern physics. The complete analogue of the Landau two-fluid hydrodynamic equations, including various transport coefficients associated with the normal fluid, has recently been derived for the trapped atomic Bose gases. In the next few years, experiments should be able to probe this two-fluid domain in Bose gases, a region first explored with such spectacular success in superfluid helium by Kapitza and Allen and Misener. The complexity of analyzing any liquid at a microscopic level has resulted in many aspects of the theory of superfluid.