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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Finite-temperature transport in one-dimensional quantum lattice models
Bruno Bertini,Fabian Heidrich-Meisner,Christoph Karrasch,Tomaž Prosen,Robin Steinigeweg,Marko Žnidarič +5 more
TL;DR: In this paper, a review of the current understanding of transport in one-dimensional lattice models, in particular in the paradigmatic example of the spin-1/2 XXZ and Fermi-Hubbard models, is reviewed, as well as state-of-theart theoretical methods, including both analytical and computational approaches.
Journal ArticleDOI
Quantum simulations with cold trapped ions
TL;DR: The control of internal and motional quantum degrees of freedom of laser-cooled trapped ions has been subject to intense theoretical and experimental research for about three decades as discussed by the authors, which may be employed to investigate physical models conceived to describe systems that are not directly accessible for experimental investigations.
Journal ArticleDOI
Ultracold atoms out of equilibrium
TL;DR: In this paper, the authors give an overview of the rapid experimental progress that has been made in the field over the last years and highlight some of the questions which may be explored in the future.
Journal ArticleDOI
The Bogoliubov model of weakly imperfect Bose gas
TL;DR: In this paper, the authors present a systematic account of known rigorous results about the Bogoliubov model of weakly imperfect Bose gas (WIBG) and a review of some models related to the WIBG and to the Bogiubov theory, where a similar two-stage Bose condensation may take place.
Journal ArticleDOI
Ultracold Atoms Out of Equilibrium
TL;DR: In this paper, an overview of the rapid experimental progress that has been made in the field over the past few years and highlight some of the questions that may be explored in the future.
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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