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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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
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Journal ArticleDOI
Exactly solvable models and ultracold Fermi gases
TL;DR: In this article, exactly solvable models of ultracold Fermi gases are reviewed via their thermodynamic Bethe ansatz solution, and analytical and numerical results are obtained for the thermodynamics and ground state properties of two-?and three-component one-dimensional attractive fermions with population imbalance.
Journal ArticleDOI
Solution to the initial value problem for the quantum nonlinear Schrödinger equation
Bernard Yurke,M. J. Potasek +1 more
TL;DR: In this article, the exact time evolution of an initial Schrodinger state vector is obtained for the two-particle case when the two particles initially occupy the same Gaussian wave packet.
Journal ArticleDOI
Finite-size corrections in the nonlinear Schrodinger model
A Berkovich,G Murthy +1 more
TL;DR: In this paper, a method based on the Euler-Maclaurin formula is proposed to obtain all finite-size corrections to the energies of the ground and excited states for the one-dimensional Bose gas with delta function interactions.
Journal ArticleDOI
Discrete harmonic analysis on a Weyl alcove
J. F. van Diejen,E. Emsiz +1 more
TL;DR: In this article, a representation of the double affine Hecke algebra at the critical level q = 1 in terms of difference-reflection operators was introduced and used to construct an explicit integrable discrete Laplacian on the Weyl alcove corresponding to an element in the center.
Journal ArticleDOI
Ground states of dipolar gases in quasi-one-dimensional ring traps
TL;DR: In this paper, the ground state of dipoles in a quasi-one-dimensional ring trap is computed using few-body techniques combined with analytical arguments, and the effect of inhomogeneities based on a local-density approximation is discussed.
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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