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
Lectures on Yangian Symmetry
TL;DR: Yangian symmetry has been used in quantum, two-dimensional field theories as discussed by the authors, where the Yangian algebra is implemented as a Hopf algebra and its generators are renormalized.
Journal ArticleDOI
Colloquium : Multiconfigurational time-dependent Hartree approaches for indistinguishable particles
TL;DR: In this article, a theory and associated practical numerical approaches to treat the time-dependent Schrodinger equation for identical interacting particles from first principles and their use in atomic and molecular systems are discussed.
Journal ArticleDOI
Exact methods in the analysis of the non-equilibrium dynamics of integrable models: application to the study of correlation functions for non-equilibrium 1D Bose gas
TL;DR: In this article, the authors study the non-equilibrium dynamics of one-dimensional Bose gas from the general perspective of the dynamics of integrable systems and develop a numerical procedure which allows explicit summation over intermediate states and analysis of the time evolution of non-local density correlation functions.
Journal ArticleDOI
Exact relaxation dynamics of a localized many-body state in the 1D Bose gas.
TL;DR: Through an exact method, the time evolution of the density profile for an initially localized state in the one-dimensional bosons with repulsive short-range interactions is solved and a localized state with a density notch is constructed by superposing one-hole excitations.
Journal ArticleDOI
Analytical expression for a post-quench time evolution of the one-body density matrix of one-dimensional hard-core bosons
J. De Nardis,Jean-Sébastien Caux +1 more
TL;DR: In this paper, 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.
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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