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
Citations
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Journal ArticleDOI
Exact Analysis of a δ-Function Spin-1/2 Attractive Fermi Gas with an External Magnetic Field
Toshiaki Iida,Miki Wadati +1 more
TL;DR: In this paper, the authors studied the excitation spectrum of a one-dimensional δ-function attractive spin-1/2 fermions by the thermal Bethe ansatz method at zero temperature.
Journal ArticleDOI
Bethe Ansatz Matrix Elements as Non-Relativistic Limits of Form Factors of Quantum Field Theory
TL;DR: In this article, the matrix elements of integrable models computed by the Algebraic Bethe Ansatz can be put in direct correspondence with the Form Factors of Integrable relativistic field theories.
Journal ArticleDOI
Holographic optical traps for atom-based topological Kondo devices
Francesco Buccheri,Graham D. Bruce,Andrea Trombettoni,Donatella Cassettari,Hrachya M. Babujian,Hrachya M. Babujian,Vladimir E. Korepin,Vladimir E. Korepin,Pasquale Sodano +8 more
TL;DR: In this article, a junction of crossed Tonks-Girardeau gases arranged in a star-geometry (forming a Y -junction) is considered and a theoretical analysis of this junction is performed, showing that it provides a physical realization of the topological Kondo model in the realm of cold atom systems.
Posted Content
An exactly solvable quantum four-body problem associated with the symmetries of an octacube
TL;DR: In this article, it was shown that the eigengies and eigenstates of a system consisting of four one-dimensional hard-core particles with masses of 6m, 2m, $m, and 3m in a hard-wall box can be found exactly using Bethe Ansatz.
Journal ArticleDOI
Critical analysis of the Bogoliubov theory of superfluidity
Stephan Adams,Jean-Bernard Bru +1 more
TL;DR: In this article, a new constructive critical analysis of the Bogoliubov theory is performed to come to a better model, which is the origin of an improvement of the previous theory for which we verify the physical arguments.
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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