Journal ArticleDOI
Exact analysis of an interacting bose gas. i. the general solution and the ground state
Elliott H. Lieb,Werner Liniger +1 more
TLDR
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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Posted Content
The Ground State Energy of a Dilute Bose Gas
Elliott H. Lieb,Jakob Yngvason +1 more
TL;DR: In this paper, the ground state energy per particle of an interacting, dilute Bose gas at density ρ 2 ρ a/m was shown to decrease faster than ρ 1/r^3 at infinity.
Journal ArticleDOI
Time-dependent multipoint correlation functions of the nonlinear Schrödinger model
A. Berkovich,G. Murthy +1 more
TL;DR: In this paper, a one-dimensional system of bosons, interacting via a delta-function potential, is analyzed by means of a conformal field theory approach, and a systematic method for deriving the operator content of the critical Hamiltonian of the model is proposed.
Journal ArticleDOI
An exact reformulation of the Bose–Hubbard model in terms of a stochastic Gutzwiller ansatz
Iacopo Carusotto,Yvan Castin +1 more
TL;DR: In this paper, the authors extended the exact reformulation of the bosonic many-body problem in terms of a stochastic Hartree ansatz for the Bose-Hubbard model.
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Orthogonality of Bethe Ansatz eigenfunctions for the Laplacian on a hyperoctahedral Weyl alcove
J. F. van Diejen,E. Emsiz +1 more
TL;DR: The orthogonality of the Bethe Ansatz eigenfunctions for the Laplacian on a hyper-octahedral Weyl alcove with repulsive homogeneous Robin boundary conditions at the walls was proved in this article.
Journal ArticleDOI
Partition function for a one-dimensional δ-function Bose gas
Go Kato,Miki Wadati +1 more
TL;DR: The N-particle partition function of a one-dimensional delta-function Bose gas is calculated explicitly using only the periodic boundary condition (the Bethe ansatz equation) and the N- particles cluster integrals are shown to be the same as those by the thermal Bethe Ansatz method.
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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