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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Spectral theory for the -Boson particle system
TL;DR: In this article, the authors developed spectral theory for the generator of the -Boson results to a discrete delta Bose gas considered previously by van Diejen, as well as to another discrete delta-Bose gas that describes the evolution of moments of the semi-discrete stochastic heat equation (or equivalently, the O’Connell-Yor semidiscrete directed polymer partition function).
Journal ArticleDOI
Form factor expansion for thermal correlators
Balázs Pozsgay,Gábor Takács +1 more
TL;DR: In this paper, the authors considered finite temperature correlation functions in massive integrable quantum field theory and developed a novel approach (based on multi-dimensional residues) to the form factor expansion for thermal correlators.
Journal ArticleDOI
Generalized Hydrodynamics with Space-Time Inhomogeneous Interactions
TL;DR: In this article, a generalized hydrodynamics (GHD) framework is proposed to describe out-of-equilibrium integrable systems with space-time inhomogeneous interactions.
Journal ArticleDOI
Analytical expression for a post-quench time evolution of the one-body density matrix of one-dimensional hard-core bosons
TL;DR: In this article, the authors apply the logic of the quench action to give an exact analytical expression for the time evolution of the one-body density matrix after an interaction quench in the Lieb-Liniger model from the ground state of the free theory (BEC state) to the infinitely repulsive regime.
Journal ArticleDOI
Local correlations in a strongly interacting one-dimensional Bose gas
TL;DR: In this article, an analytical method for calculating local correlations in strongly interacting one-dimensiona l( 1D) Bose gases, based on the exactly solvable Lieb-Liniger model, was developed.
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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