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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Journal ArticleDOI
Diagonalization of an Integrable Discretization of the Repulsive Delta Bose Gas on the Circle
TL;DR: In this article, an integrable lattice discretization of the quantum system of n bosonic particles on a ring interacting pairwise via repulsive delta potentials is introduced, and the corresponding (finite-dimensional) spectral problem is solved by means of the Bethe Ansatz method.
Journal ArticleDOI
Form factor expansion for thermal correlators
Balázs Pozsgay,Gábor Takács +1 more
TL;DR: In this article, 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
Metastable quantum phase transitions in a periodic one-dimensional Bose gas: II. Many-body theory
TL;DR: In this paper, it was shown that quantum solitons in the Lieb-Liniger Hamiltonian are precisely the yrast states of the Bose gas, and that the metastable quantum phase transition in mean-field analysis of the weakly interacting Hamiltonian extends into the medium-to strongly interacting regime of a periodic one-dimensional bose gas.
Journal ArticleDOI
From the sinh-Gordon field theory to the one-dimensional Bose gas: exact local correlations and full counting statistics
TL;DR: In this article, the expectation value of local observables in a one-dimensional gas of bosons with point-wise repulsive interactions was derived for all excited states in the thermodynamic limit, including thermal states, generalized Gibbs ensembles and non-equilibrium steady states arising in transport settings.
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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