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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Journal ArticleDOI
Euler-scale dynamical correlations in integrable systems with fluid motion
TL;DR: In this article, an iterative scheme for numerically calculating dynamical two-point correlation functions in integrable many-body systems, in the Eulerian scaling limit, was devised.
Journal ArticleDOI
Thermalization of a quantum Newton's cradle in a one-dimensional quasicondensate
TL;DR: In this paper, the authors studied the nonequilibrium dynamics of the quantum Newton's cradle in a one-dimensional Bose gas in the weakly interacting quasicondensate regime.
Journal ArticleDOI
Two-time height distribution for 1D KPZ growth: the recent exact result and its tail via replica
TL;DR: In this article, the authors studied the joint probability distribution function (JPDF) of the interface heights at two times $t_1$ and $t-2>t-1$ with droplet initial conditions at $t=0.
Journal ArticleDOI
Ground state energy of the $\delta$-Bose and Fermi gas at weak coupling from double extrapolation
TL;DR: In this paper, the ground state energy of the Lieb-Liniger gas with δ-interaction was derived for the weak coupling regime, where δ = 0.00158769986550594498929.
Journal ArticleDOI
Interacting ultracold atomic kicked rotors: loss of dynamical localization
TL;DR: In this article, the fate of dynamical localization of two quantum-kicked rotors with contact interaction was studied, which relates to experimental realizations of the rotors using ultra-cold atomic gases.
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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