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
Integrable families of hard-core particles with unequal masses in a one-dimensional harmonic trap
Nathan Harshman,Nathan Harshman,Maxim Olshanii,A. S. Dehkharghani,Artem G. Volosniev,Steven Glenn Jackson,Nikolaj T. Zinner +6 more
TL;DR: In this paper, it was shown that the dynamics of particles in a one-dimensional harmonic trap with hard-core interactions can be solvable for certain arrangements of unequal masses, and for any number of particles, there exist two families of unequal mass particles that have integrable dynamics, and there are additional exceptional cases for three, four and five particles.
Journal ArticleDOI
Bound states of dipolar bosons in one-dimensional systems
Artem G. Volosniev,J. R. Armstrong,J. R. Armstrong,D. V. Fedorov,A. S. Jensen,Manuel Valiente,Nikolaj Thomas Zinner +6 more
TL;DR: In this paper, one-dimensional tubes containing bosonic polar molecules are considered and the long-range dipole?dipole interactions act both within a single tube and between different tubes.
Journal ArticleDOI
Excitations in two-component Bose-gases
TL;DR: In this paper, a strongly correlated quantum system that has become amenable to experiment by the advent of ultracold bosonic atoms in optical lattices, a chain of two different bosonic constituents, was considered within the framework of bosonization and Luttinger liquid theory.
Book ChapterDOI
BCS–BEC Crossover and Unconventional Superfluid Order in One Dimension
TL;DR: In this paper, the BCS-BEC crossover in one-dimensional Fermi gases is discussed and exact results using the Bethe Ansatz as well as numerical calculations of the correlation functions and the complete phase diagram are presented.
Journal ArticleDOI
On the Riemann-Hilbert approach to the asymptotic analysis of the correlation functions of the Quantum Nonlinear Schrodinger equation. Non-free fermionic case
TL;DR: In this paper, the local field dynamical temperature correlation function of the Quantum Nonlinear Schrodinger equation with the finite coupling constant was considered and the related operator-valued Riemann-Hilbert problem was used for analysing the leading term of the large time and long distance asymptotics of the correlation function.
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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