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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Surface free energy of the open XXZ spin-1/2 chain
TL;DR: In this article, the authors studied the boundary free energy of the XXZ spin-1/2 chain subject to diagonal boundary fields and derived a representation for the surface free energy which involves the solution of the non-linear integral equation that governs the thermodynamics of the spin 1/2 chains subject to periodic boundary conditions.
Journal ArticleDOI
Theory of superfluidity and drag force in the one-dimensional Bose gas
TL;DR: In this article, the drag force obtained from linear response theory in relation to Landau's criterion of superfluidity is discussed, based upon improved analytical and numerical understanding of the dynamical structure factor, results for different obstacle potentials are obtained, including single impurities, optical lattices and random potentials generated from speckle patterns.
Journal ArticleDOI
Quantum dynamics of Bose-Hubbard Hamiltonians beyond the Hartree-Fock-Bogoliubov approximation: The Bogoliubov back-reaction approximation
TL;DR: In this article, a method for studying the quantum field dynamics of ultracold Bose gases confined within optical lattice potentials, within the lowest Bloch-band Bose-Hubbard model, was proposed.
Journal ArticleDOI
Diffusion in generalized hydrodynamics and quasiparticle scattering
TL;DR: In this paper, the authors extend the hydrodynamic theory for quantum and classical integrable models to account for diffusive dynamics and local entropy production, and show that the diffusion is due to scattering processes among quasiparticles, which are only present in truly interacting systems.
Journal ArticleDOI
On Form Factors in nested Bethe Ansatz systems
TL;DR: In this article, the form factors of local operators in the multi-component Quantum Non-linear Schrodinger model were investigated, a prototype theory solvable by the so-called nested Bethe Ansatz.
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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