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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Linearized regime of the generalized hydrodynamics with diffusion
Miłosz Panfil,Jacek Pawełczyk +1 more
TL;DR: In this paper, the generalized hydrodynamics including the diffusion term for an initially inhomogeneous state in the Lieb-Liniger model were considered and a general solution was constructed in terms of the eigenstates of the evolution operator and two prototypical classes of initial states: delocalized and localized spatially.
Journal ArticleDOI
Off-diagonal correlations in one-dimensional anyonic models: A replica approach
TL;DR: In this article, a generalization of the replica trick was proposed to calculate the large distance asymptotics of off-diagonal correlation functions in anyonic models with a proper factorizable ground-state wave function.
Journal ArticleDOI
Collective dispersion relations for the 1D interacting two-component Bose and Fermi gases
M. Bortz,N. Oelkers +1 more
TL;DR: In this article, the elementary excitations of charge and spin degrees for the 1D interacting two-component Bose and Fermi gases were investigated by means of the discrete Bethe ansatz equations.
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Exact Solutions for Some Nuclear Many-Body Problems
Feng Pan,Jerry P. Draayer +1 more
TL;DR: In this paper, exact solutions for eigenvalues and eigenfunctions of some nuclear many-body systems are found by using an infinite-dimensional, Lie-algebraic approach based on the corresponding Bethe ansatz.
Journal ArticleDOI
The Dynamics of the One-Dimensional Delta-Function Bose Gas
Craig A. Tracy,Harold Widom +1 more
TL;DR: In this paper, a method to solve the time-dependent Schroedinger equation for a system of one-dimensional bosons interacting via a repulsive delta function potential was proposed, using the ideas of Bethe Ansatz but does not use the spectral theory of the associated Hamiltonian.
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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