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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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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Integral equations for correlation functions of a quantum one-dimensional Bose gas
TL;DR: In this article, the large-time, long-distance behavior of the temperature correlation functions of a quantum one-dimensional Bose gas is considered and integral equations which are closely related to the thermodynamic Bethe ansatz equations and whose solutions describe asymptotic expressions are obtained.
Journal ArticleDOI
Non Relativistic Limit of Integrable QFT and Lieb-Liniger Models
TL;DR: In this article, a suitable limit of integrable QFT with the aim to identify continuous non-relativistic integrably QFT models with local interactions was proposed. But the model is not considered in this paper.
Journal ArticleDOI
Correlations of zero-entropy critical states in the XXZ model: integrability and Luttinger theory far from the ground state
TL;DR: In this article, a detailed study of static and dynamical spin-spin correlations is presented, and the correlations obtained directly from integrability and those emerging from the Luttinger field theory description are shown to be in extremely good correspondence, as expected, for the large distance asymptotics, but surprisingly also for the short distance behavior.
Journal ArticleDOI
Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution
TL;DR: In this article, the Bethe-Ansatz equations were solved in the thermodynamic limit by using an analytic method based on a series expansion on orthogonal polynomials.
Journal ArticleDOI
Pump-probe spectroscopy of Bose polarons: Dynamical formation and coherence
TL;DR: In this paper, a pump-probe spectroscopy scheme was proposed for monitoring the time-resolved dynamics of polaronic excitations by utilizing impurity atoms with spin-dependent interactions with their environment.
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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