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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Correlation functions of the chiral Potts chain from conformal field theory and finite-size corrections
TL;DR: In this article, the authors studied the incommensurate phase of the N = 3 superintegrable chiral Potts chain by computing the leading finite-size corrections to the low-lying energy levels.
Journal ArticleDOI
Tail of the two-time height distribution for KPZ growth in one dimension
TL;DR: In this article, the authors studied the joint probability distribution function (JPDF) of the height of the KPZ equation with droplet initial conditions, at two different times $t 1
Journal ArticleDOI
Probing an ultracold-atom crystal with matter waves
TL;DR: In this paper, the same principle was used for probing the strongly correlated phases of ultracold atoms confined to optical lattices, and the results showed that it offers a valuable and potentially non-destructive tool to characterize underlying spatial order.
Journal ArticleDOI
Two-dimensional O(3) model at nonzero density: From dual lattice simulations to repulsive bosons
TL;DR: In this article, the thermodynamics of the O(3) nonlinear sigma model at nonzero chemical potential (equivalent to a magnetic field) were discussed and a quantum phase transition at zero temperature where as a function of the chemical potential the density assumes a nonzero value.
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Integrability breakdown in longitudinaly trapped, one-dimensional bosonic gases
TL;DR: In this paper, a system of identical bosons with short-range (contact) interactions is studied and their motion is confined to one dimension by a tight lateral trapping potential and, additionally, subject to a weak harmonic confinement in the longitudinal direction.
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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Atomic Scattering in the Presence of an External Confinement and a Gas of Impenetrable Bosons
Maxim Olshanii,Maxim Olshanii +1 more