Journal ArticleDOI
Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum
TLDR
In this paper, the analysis of the one-dimensional gas of Bose particles interacting via a repulsive delta function potential by considering the excitation spectrum was carried out and it was shown that the elementary excitations are most naturally thought of as a double spectrum, not a single one.Abstract:
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.read more
Citations
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Journal ArticleDOI
Many-Body Physics with Ultracold Gases
TL;DR: In this article, a review of recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases is presented, focusing on effects beyond standard weakcoupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation.
Journal ArticleDOI
Exact analysis of an interacting bose gas. i. the general solution and the ground state
Elliott H. Lieb,Werner Liniger +1 more
TL;DR: In this paper, the ground-state energy as a function of γ was derived for all γ, except γ = 0, and it was shown that Bogoliubov's perturbation theory is valid when γ is small.
Quantum Inverse Scattering Method and Correlation Functions
TL;DR: One-dimensional Bose-gas One-dimensional Heisenberg magnet Massive Thirring model Classical r-matrix Fundamentals of inverse scattering method Algebraic Bethe ansatz Quantum field theory integral models on a lattice Theory of scalar products Form factors Mean value of operator Q Assymptotics of correlation functions Temperature correlation functions Appendices References as discussed by the authors
Journal ArticleDOI
Thermodynamics of a One‐Dimensional System of Bosons with Repulsive Delta‐Function Interaction
Chen Ning Yang,C.P. Yang +1 more
TL;DR: In this paper, the equilibrium thermodynamics of a one-dimensional system of bosons with repulsive delta function interaction was derived from the solution of a simple integral equation, and the excitation spectrum at any temperature T was also found.
Journal ArticleDOI
One-dimensional Fermi liquids
TL;DR: In this article, the authors review the progress in the theory of one-dimensional (ID) Fermi liquids which has occurred over the past decade and present a description of the low-energy properties of gapless 1D quantum systems can be based on the exactly solvable Luttinger model which incorporates these features, and whose correlation functions can be calculated.
References
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Journal ArticleDOI
Exact analysis of an interacting bose gas. i. the general solution and the ground state
Elliott H. Lieb,Werner Liniger +1 more
TL;DR: In this paper, the ground-state energy as a function of γ was derived for all γ, except γ = 0, and it was shown that Bogoliubov's perturbation theory is valid when γ is small.
Journal ArticleDOI
Relationship between Systems of Impenetrable Bosons and Fermions in One Dimension
TL;DR: In this article, a rigorous one-one correspondence between one-dimensional systems of bosons and spinless fermions is established, subject only to the restriction that the interaction has an impenetrable core.
Journal ArticleDOI
Atomic Theory of the Two-Fluid Model of Liquid Helium
TL;DR: In this article, it was argued that the wave function representing an excitation in liquid helium should be nearly of the form Σif(ri)φ, where φ is the ground-state wave function, f(r) is some function of position, and the sum is taken over each atom i.i.
Journal ArticleDOI
Atomic theory of the lambda transition in helium
TL;DR: In this paper, it is shown from first principles that liquid He4 should exhibit a transition analogous to the transition in an ideal Bose-Einstein gas, and the exact partition function is written as an integral over trajectories, using the space-time approach to quantum mechanics.
Journal ArticleDOI
Atomic theory of liquid helium near absolute zero
TL;DR: In this paper, the properties of liquid helium at very low temperatures (below 0.5°K) were discussed from the atomic point of view, and it was argued that the lowest states are compressional waves (phonons).
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