Journal ArticleDOI
Exact analysis of an interacting bose gas. i. the general solution and the ground state
Elliott H. Lieb,Werner Liniger +1 more
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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
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Journal ArticleDOI
Quantum time crystals.
TL;DR: Some subtleties and apparent difficulties associated with the notion of spontaneous breaking of time-translation symmetry in quantum mechanics are identified and resolved and a model exhibiting that phenomenon is displayed.
Journal ArticleDOI
Dynamics of a quantum phase transition and relaxation to a steady state
TL;DR: In this paper, the authors review recent theoretical work on two closely related issues: excitation of an isolated quantum condensed matter system driven adiabatically across a continuous quantum phase transition or a gapless phase and apparent relaxation of an excited system after a sudden quench of a parameter in its Hamiltonian.
Journal ArticleDOI
Un systeme a une dimension de fermions en interaction
TL;DR: In this article, the systeme de N fermions de spin 1 2, de meme masse, en interaction δ sur un cercle de longueur L. Nous presentons dans cette note les equations couplees qui determinent les niveaux denergie of ce systeme for toutes les valeurs du spin total S, generalisant ainsi les resultats obtenus par Mc. Guire [1] for S = 1 2 N−1.
Journal ArticleDOI
Fermi gases in one dimension: From Bethe ansatz to experiments
TL;DR: In this paper, theoretical and experimental developments for one-dimensional Fermi gases are discussed. But the exact results obtained for Bethe ansatz integrable models of this kind enable the study of the nature and microscopic origin of a wide range of quantum many-body phenomena driven by spin population imbalance, dynamical interactions, and magnetic fields.
Journal ArticleDOI
Proof of Bose-Einstein condensation for dilute trapped gases.
Elliott H. Lieb,Robert Seiringer +1 more
TL;DR: This work proves theoretically for bosons with two-body repulsive interaction potentials in the dilute limit that the condensation is 100% into the state that minimizes the Gross-Pitaevskii energy functional.
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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