Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Springer eBooks

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

Élliott H. Lieb

Published Jan 1, 2004• 33 citations
Publisher
DOI
10.1007/978-3-662-06390-3_37

Related papers

WITHDRAWN: Exact Analysis of an Interacting Bose Gas.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

Élliott H. Lieb

Elsevier eBooks•Jan 1, 1966•0 citations

The Interaction Effect on the Excitation Spectrum of Homogeneous Bose Gas

Lan Yin, Tin-Lun Ho

APS•Mar 1, 2001•0 citations

Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State

Élliott H. Lieb, Werner Liniger

Springer eBooks•Jan 1, 2004•118 citations

Excitation Spectrum for Weakly Interacting Bose Gas and the Liquid Structure Function of Helium

A. Bhattacharyya, Chia-Wei Woo

Springer eBooks•Jan 1, 1974•1 citation

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 Review•May 15, 1963•1,083 citations

Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State

Élliott H. Lieb, Werner Liniger

A gas of one-dimensional Bose particles interacting via a repulsive delta-function potential has been solved exactly. All the eigenfunctions can be found explicitly and the energies are given by the solutions of a transcendental equation. The problem has one nontrivial coupling constant, $\ensuremath{\gamma}$. When $\ensuremath{\gamma}$ is small, Bogoliubov's perturbation theory is seen to be valid. In this paper, we explicitly calculate the ground-state energy as a function of $\ensuremath{\gamma}$ and show that it is analytic for all $\ensuremath{\gamma}$, except $\ensuremath{\gamma}=0$. In Part II, we discuss the excitation spectrum and show that it is most convenient to regard it as a double spectrum---not one as is ordinarily supposed.

Physical Review•May 15, 1963•2,707 citations
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.
A gas of one-dimensional Bose particles interacting via a repulsive delta-function potential has been solved exactly. All the eigenfunctions can be found explicitly and the energies are given by the solutions of a transcendental equation. The problem has one nontrivial coupling constant, $\ensuremath{\gamma}$. When $\ensuremath{\gamma}$ is small, Bogoliubov's perturbation theory is seen to be valid. In this paper, we explicitly calculate the ground-state energy as a function of $\ensuremath{\gamma}$ and show that it is analytic for all $\ensuremath{\gamma}$, except $\ensuremath{\gamma}=0$. In Part II, we discuss the excitation spectrum and show that it is most convenient to regard it as a double spectrum---not one as is ordinarily supposed.