Microscopic Analysis of Interacting Elementary Excitations in Bose Systems.

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.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

Nonanalytic Elementary Excitation Spectrum at Long Wavelengths in a Bose Gas and Liquid He4

Harvey Gould, Victor K. Wong

A rigorous microscopic analysis of a weakly interacting Bose gas at zero temperature shows that the elementary excitation spectrum $\ensuremath{\omega}(k)$ is not an analytic function of the wave vector $k$ in the long-wavelength limit but has the form $k[{c}_{0}+{c}_{2}{k}^{2}+{c}_{L4}{k}^{4}\mathrm{ln}(\frac{1}{k})+\ensuremath{\cdots}]$. It is pointed out that the structure factor $S(k)$ is not an analytic function of $k$ and that the specific heat ${C}_{v}(T)$ at low temperatures $T$ has the form ${C}_{v}={T}^{3}[{C}_{0}+{C}_{2}{T}^{2}+{C}_{L4}{T}^{4}\mathrm{ln}(\frac{1}{T})+\ensuremath{\cdots}]$. The extension of these results to liquid ${\mathrm{He}}^{4}$ is discussed.A rigorous microscopic analysis of a weakly interacting Bose gas at zero temperature shows that the elementary excitation spectrum $\ensuremath{\omega}(k)$ is not an analytic function of the wave vector $k$ in the long-wavelength limit but has the form $k[{c}_{0}+{c}_{2}{k}^{2}+{c}_{L4}{k}^{4}\mathrm{ln}(\frac{1}{k})+\ensuremath{\cdots}]$. It is pointed out that the structure factor $S(k)$ is not an analytic function of $k$ and that the specific heat ${C}_{v}(T)$ at low temperatures $T$ has the form ${C}_{v}={T}^{3}[{C}_{0}+{C}_{2}{T}^{2}+{C}_{L4}{T}^{4}\mathrm{ln}(\frac{1}{T})+\ensuremath{\cdots}]$. The extension of these results to liquid ${\mathrm{He}}^{4}$ is discussed.

Physical Review LettersAug 9, 197116 citations

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.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

k

in the long-wavelength limit but has the form $k[{c}_{0}+{c}_{2}{k}^{2}+{c}_{L4}{k}^{4}\mathrm{ln}(\frac{1}{k})+\ensuremath{\cdots}]$. It is pointed out that the structure factor

S(k)

is not an analytic function of

k

and that the specific heat

{C}_{v}(T)

at low temperatures

T

has the form ${C}_{v}={T}^{3}[{C}_{0}+{C}_{2}{T}^{2}+{C}_{L4}{T}^{4}\mathrm{ln}(\frac{1}{T})+\ensuremath{\cdots}]$. The extension of these results to liquid

{\mathrm{He}}^{4}

is discussed.