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
One-dimensional mixtures of several ultracold atoms: a review
TL;DR: The recent advances on trapped Bose-Fermi mixtures are described, which allow for a theoretical combination of previous concepts, well illustrating the importance of quantum statistics and inter-particle interactions.
Journal ArticleDOI
Exciton correlations in coupled quantum wells and their luminescence blue shift
Boris Laikhtman,Ronen Rapaport +1 more
TL;DR: In this article, the authors present a study of an exciton system where electrons and holes are confined in double quantum well structures, and they show that the tail of this interaction leads to a strong correlation between excitons and substantially affects the behavior of the system.
Journal ArticleDOI
The Excitation Spectrum for Weakly Interacting Bosons
TL;DR: In this paper, the authors investigated the low energy excitation spectrum of a Bose gas with weak, long range repulsive interactions and proved that the Bogoliubov spectrum of elementary excitations with linear dispersion relation for small momentum becomes exact in the mean-field limit.
Journal ArticleDOI
Fermionization of two-component few-fermion systems in a one-dimensional harmonic trap
TL;DR: In this article, the properties of a single spin-down atom interacting with a number of spin-up particles were investigated in a one-dimensional harmonic trap with a new rapidly converging effective-interaction technique.
Journal ArticleDOI
Stationary Correlations for the 1D KPZ Equation
TL;DR: In this article, the exact stationary properties of the one-dimensional Kardar-Parisi-Zhang (KPZ) equation were studied by using the replica approach, where the stationary state for the KPZ equation was realized by setting the initial condition the two-sided Brownian motion (BM) with respect to the space variable.
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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