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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Non-Hermitian Luttinger liquids and flux line pinning in planar superconductors
TL;DR: In this article, the effect of a single columnar defect on vortex filaments oriented parallel to the surface of a thin planar superconductor was studied and a delicate interplay between enhancement of pinning due to Luttinger liquid effects and depinning due to the tilted magnetic field was uncovered.
Journal ArticleDOI
A perturbed mean field model of an interacting boson gas and the large deviation principle
TL;DR: In this paper, the equilibrium thermodynamics of a mean field model of an interacting boson gas perturbed by a term quadratic in the occupation numbers of the free gas energy-levels were studied.
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Gases in two dimensions: universal thermodynamics and its consequences
TL;DR: In this article, the authors discuss ideal and interacting quantum gases obeying general fractional exclusion statistics, and show that the microscopic reason for this equivalence is a one-to-one correspondence between the excited states of these systems.
Journal ArticleDOI
Ground State of 1D Bosons with Delta Interaction: Link to the BCS Model
TL;DR: In this article, the ground-state energy of the integrable one-dimensional (1D) model of interacting bosons with weakly repulsive two-body delta interactions are seen to satisfy the set of Richardson equations appearing in the strong coupling limit of an integrably BCS pairing model.
Journal ArticleDOI
On the ground state energy of the δ-function Bose gas
Craig A. Tracy,Harold Widom +1 more
TL;DR: In this paper, the weak coupling asymptotics of the ground state energy of the Bose gas were derived using the electrostatic interpretation of the Lieb-Liniger integral equation.
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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