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
Citations
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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
Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles.
TL;DR: In this article, a review is devoted to the problem of thermalization in a small isolated conglomerate of interacting constituents, where statistical regularities come into play through inter-particle interactions, which have two fundamental components: mean field and residual interactions responsible for the complex structure of actual stationary states.
Journal ArticleDOI
A one-dimensional liquid of fermions with tunable spin
Guido Pagano,Marco Mancini,G. Cappellini,Pietro Lombardi,Florian Schäfer,Hui Hu,Xia-Ji Liu,Jacopo Catani,Carlo Sias,Massimo Inguscio,Leonardo Fallani +10 more
TL;DR: In this article, an ultracold atom experiment investigates the behavior of one-dimensional strongly correlated fermions with a tunable number of spin components, and the results show that strongly correlated Fermions have a similar behavior as strongly correlated many-body systems.
Book ChapterDOI
Exactly Solvable Models in Statistical Mechanics
Miki Wadati,Yasuhiro Akutsu +1 more
TL;DR: In this article, it was shown that there exists an infinite number of exactly solvable models in 2-dimen-sional statistical mechanics and a brief summary of the quantum inverse scattering method is given to emphasize the soliton theoretic aspect of the theory.
Journal ArticleDOI
Ultradilute Low-Dimensional Liquids.
TL;DR: The Gross-Pitaevskii equation is derived to describe droplets of such liquids and solved analytically in the one-dimensional case and shows that in the case of attractive inter- and repulsive intraspecies interactions the energy per particle has a minimum at a finite density corresponding to a liquid state.
References
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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