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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A quantum Newton's cradle
TL;DR: In this paper, the authors show that a homogeneous 1D Bose gas with point-like collisional interactions is integrable, and that it is possible to construct a system with many degrees of freedom that does not reach thermal equilibrium even after thousands of collisions.
Journal ArticleDOI
Relaxation and Prethermalization in an Isolated Quantum System
Michael Gring,Maximilian Kuhnert,Tim Langen,Takuya Kitagawa,Bernhard Rauer,M. Schreitl,Igor Mazets,Igor Mazets,D. Adu Smith,Eugene Demler,Jörg Schmiedmayer +10 more
TL;DR: Measurements of full quantum mechanical probability distributions of matter-wave interference are used to study the relaxation dynamics of a coherently split one-dimensional Bose gas and obtained comprehensive information about the dynamical states of the system.
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One dimensional bosons: From condensed matter systems to ultracold gases
TL;DR: The physics of one-dimensional interacting bosonic systems is reviewed in this paper, where the effects of various perturbations on the Tomonaga-Luttinger liquid state are discussed as well as extensions to multicomponent and out of equilibrium situations.
Journal ArticleDOI
Exact results in the theory of magnetic alloys
A. M. Tsvelick,Paul Wiegmann +1 more
TL;DR: In this paper, a detailed account of the Bethe-Ansatz technique for the s-d exchange (Kondo) model with arbitrary impurity spin, s-D model with anisotropic exchange, degenerate exchange model and for the canonical Anderson model is given.
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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