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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One-dimensional w-component fermions and bosons with repulsive delta function interaction
TL;DR: For 1D Bosons with repulsive delta function interaction with any number of components and any Young tableau, the energy per particle as N → ∞ is the same as for spinless Bosons as discussed by the authors.
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Quantum quenches to the attractive one-dimensional Bose gas: exact results
TL;DR: In this article, the authors studied the properties of the stationary state reached at late times after the quench, which displays a finite density of multi-particle bound states, whose rapidity distribution is determined exactly by means of the quen action method.
Journal ArticleDOI
The form factors in the finite volume
TL;DR: In this paper, the form factors of integrable models in finite volume were studied and the explicite representations for the form factor in terms of determinants were constructed for finite volume models.
Journal ArticleDOI
Quantum nonlinear Schrödinger equation: Two solutions
TL;DR: The quantum nonlinear Schrodinger equation (QNLS) has attracted much attention recently as a simple exactly soluble nonlinear model of the quantum field theory in 1 + 1 space-time.
Journal ArticleDOI
Nucleation in finite topological systems during continuous metastable quantum phase transitions.
TL;DR: This work shows how to nucleate the transition between ring currents and dark soliton states in a toroidally trapped Bose-Einstein condensate by explicit global breaking of the rotational symmetry.
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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