Journal ArticleDOI
Exact analysis of an interacting bose gas. i. the general solution and the ground state
Elliott H. Lieb,Werner Liniger +1 more
TLDR
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.Abstract:
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, γ. When γ 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 γ and show that it is analytic for all γ, except γ=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.read more
Citations
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Dissertation
New phenomena in non-equilibrium quantum physics
TL;DR: In this paper, the authors proposed a framework to understand non-equilibrium quantum systems from both theoretical and experimental point of view, and they found that the applications of quantum physics are mostly limited to equilibrium or static systems.
Journal ArticleDOI
Exotic pairing in 1D spin-3/2 atomic gases with SO(4) symmetry
TL;DR: In this article, a new SO(4) symmetry integrable point in the spin-3/2 Fermi gas was found and the exact solution of the model was derived using the Bethe ansatz.
Journal ArticleDOI
The one-dimensional Coulomb problem
G. Abramovici,Yshai Avishai +1 more
TL;DR: In this paper, two methods of regularizing the singularity at x = 0 are used, yielding the same conclusion, namely, that the transmission vanishes, for both repulsive (c>0) and attractive (c<0) cases.
Journal ArticleDOI
The effect of atom losses on the distribution of rapidities in the one-dimensional Bose gas
TL;DR: In this article, the effects of atom losses in the one-dimensional Bose gas with repulsive contact interactions were investigated, and it was shown that losses affect the rapidity distribution in a non-trivial way.
Journal ArticleDOI
Lectures on Yangian Symmetry
TL;DR: Yangian symmetry in quantum field theory is discussed in this paper, where the Yangian algebra is implemented in quantum, two-dimensional field theories and its generators are renormalized.
References
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Book
A Course of Modern Analysis
TL;DR: The volume now gives a somewhat exhaustive account of the various ramifications of the subject, which are set out in an attractive manner and should become indispensable, not only as a textbook for advanced students, but as a work of reference to those whose aim is to extend the knowledge of analysis.
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
Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum
TL;DR: 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.
Journal ArticleDOI
Linear antiferromagnetic chain with anisotropic coupling
TL;DR: In this article, the exact solution for a linear chain of spin atoms coupled together by the anisotropic Hamiltonian was given for the antiferromagnetic ground state and comparison was made with a variational method.
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Atomic Scattering in the Presence of an External Confinement and a Gas of Impenetrable Bosons
Maxim Olshanii,Maxim Olshanii +1 more