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Introduction

Philippe Nozières, David Pines

Published Mar 5, 2018• 0 citations

Abstract

We begin our study of the superfluid Bose liquid with a brief review of the experimental and theoretical background of the liquid 4 He, the only Bose liquid found naturally in the laboratory. We then consider, in Chapter 2 , the quasi-particle excitations and show how at T = 0 the macroscopic occupation of the zero momentum state leads, in the long wavelength limit, to an identical excitation spectrum for quasi-particles and density fluctuations. The spectrum consists in phonons with a velocity given by the macroscopic velocity of sound. We turn in Chapter 3 to a consideration of the observed elementary excitation spectrum of He II. We discuss both the experimental measurements and the theories that have thus far been proposed to explain them.

DOI: 10.1201/9780429495717-7

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Conclusion

Philippe Nozières, David Pines

This chapter concludes the study of superfluidity in Bose liquids with a brief summary of the strengths, and of the inadequacies, of the theory. A clear understanding of the static and the long wavelength dynamic properties of an equilibrium Bose liquid, including a microscopic basis for the two-fluid model. Variational calculations of the excitation spectrum of liquid He II, which are in good quantitative agreement with experiment. A satisfactory phenomenological treatment of the interactions between elementary excitations which give rise to various irreversible phenomena. A microscopic theory of the ground state and elementary excitation spectrum of liquid He II; in fact, even the theory of the simple dilute Bose gas has not yet been extended to treat the system at finite temperatures, and under non-equilibrium situations. A clear understanding of a number of "vortex" properties, including the critical current for superfluid flow in thin capillaries.

CRC Press eBooksMar 5, 20180 citations

Conclusion

Philippe Nozières, David Pines

We conclude our study of superfluidity in Bose liquids with a brief summary of the strengths, and of the inadequacies, of the theory. The cornerstone of our fundamental understanding of superfluidity has been the recognition of the central importance of the condensate, a single quantum state which is macroscopically occupied. For the Bose liquid one has a particle condensate, characterized by a non-vanishing expectation value of ψ (r). The existence of the condensate explains all major aspects of superfluid behavior; in particular, we now possess: A clear understanding of the static and the long wavelength dynamic properties of an equilibrium Bose liquid, including a microscopic basis for the two-fluid model. A precise microscopic theory at T = 0 for a specific model, the dilute Bose gas. Variational calculations of the excitation spectrum of liquid He II (and of the ground state properties as well), which are in good quantitative agreement with experiment. A satisfactory phenomenological treatment of the interactions between elementary excitations which give rise to various irreversible phenomena. A qualitative understanding of the role which is played by quantized vortices in both equilibrium and non-equilibrium phenomena.

CRC Press eBooksMar 5, 20180 citations

First, Second, And Quasi-Particle Sound

Philippe Nozières, David Pines

We now consider the nature of the excited states of a Bose liquid at finite temperatures. In Chapters 2 and 3 , we have discussed the quasi-particle excitations at finite temperatures. We here wish to concentrate on the nature of the excited states in the long wave-length limit . As in the previous chapters, we shall restrict our attention to states for which the condensate is very nearly uniform.

CRC Press eBooksMar 5, 20180 citations

The role of pair correlations in the formation of the ground state and the elementary excitation spectrum in a superfluid Bose liquid (A Review)

Ernst A. Pashitskii

The paradoxes and disparities in the contemporary microscopic theory of superfluid helium (He–II) are discussed along with possible ways of resolving them by taking pair correlations of He4 atoms into consideration. It is shown that most paradoxes are associated with the commonly accepted initial assumption concerning the dominating role of single-particle Bose condensate (SPBC) in the quantum microstructure of the superfluid component ρs. The existence of intensive SPBC leads to a strong hybridization of the elementary excitation branches and to a common dispersion law for all boson branches, which is identified with the quasiparticle spectrum E(p) observed experimentally from slow neutron scattering in liquid helium. However, the stability of this spectrum during a transition through the λ-point and the large value of the gap in the vicinity of the “rotonic” minimum contradict both the Landau theoretical criterion of superfluidity and the small value of experimentally measured critical velocity. At the same time, a strong interaction between particles in the Bose liquid He4 strongly suppresses the SPBC which amounts to less than 1% of all He4 atoms and hence cannot be the main constituent of the superfluid component, unlike the case of a weakly nonideal Bose gas. Moreover, for a quite strong attraction between particles in a certain region of the momentum space, bound pairs of bosons can be formed in the superfluid Bose liquid, and a coherent pair condensate (CPC) analogous to the Cooper pair condensate in superconductors may appear. Such a strong CPC may completely suppress the weak SPBC. In this case, the one-particle spectrum ε(p) of elementary excitations does not hybridize with the collective (two-particle) spectrum and does not appear in the structure of the dynamic form factor S(p,ε), i.e., does not coincide with the spectrum measured from neutron scattering. The dispersion of one-particle spectrum is defined by the momentum dependence of the pair order parameter Ψ̃(p) and may have a minimum or a point of inflection at p≠0. This peculiarity in the one-particle spectrum of a Bose liquid with CPC but without SPBC vanishes together with Ψ̃(p) at the temperature Tc=Tλ of the phase transition from the superfluid to the normal state (unlike the rotonic minimum in the collective spectrum), while the corresponding critical velocity vc=min[ε(p)/p] vanishes at the λ-point in accordance with the Landau criterion and the experimental data. The assumption that the strong “Cooper-like” CPC is responsible for the quantum structure of the superfluid component ρs is confirmed indirectly by the successful application of the Justrow approximation (based on strong pair correlations) for describing the properties of liquid He4 and quantum liquid mixtures He3–4He on one hand, and by an anomalously large effective mass of He3 impurity atoms in He4, which is approximately equal to total mass of He3 and He4 atoms, thus pointing to the existence of helium atoms in superfluid liquid He–II. The value of the superfluid velocity circulation quantum in the Onsager–Feynman vortices in a Bose liquid with CPC but without SPBC is discussed as well as the critical velocities of superfluid He4 in ultrathin films and channels in which the creation and motion of quantum vortices are ruled out, and the quasiparticle spectrum undergoes dimensional quantization.

Low Temperature PhysicsFeb 1, 199914 citations

Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum

Élliott H. Lieb

We continue the analysis of the one-dimensional gas of Bose particles interacting via a repulsive delta function potential by considering the excitation spectrum. Among other things we show that: (i) the elementary excitations are most naturally thought of as a double spectrum, not a single one; (ii) the velocity of sound derived from the macroscopic compressibility is shown to agree with the velocity of sound derived from microscopic considerations, i.e., from the phonon spectrum. We also introduce a distinction between elementary excitations and quasiparticles, on the basis of which we give some heuristic reasons for expecting the double spectrum to be a general feature, even in three dimensions, and not an exception.

Physical ReviewMay 15, 19631,083 citations

Superfluid Flow: Macroscopic Limit

Philippe Nozières, David Pines

In the preceding chapters, we have been mostly concerned with the ground state, |0〉, of a Bose liquid; we have discussed at length its structure, its excitation spectrum, and its response to a weak external probe. We have seen that all these properties were deeply influenced by the existence of a condensate , consisting in the n o particles which occupy the single state k = 0. Such a condensate is clearly at rest; it possesses a uniform density and carries no current.

CRC Press eBooksMar 5, 20180 citations