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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Towards a rigorous derivation of the cubic NLSE in dimension one
TL;DR: In this paper, the finite and the infinite Schrodinger hierarchies for the reduced density matrices of subsystems with n particles were constructed, and it was shown that the solution of the finite hierarchy converges in a suitable sense to a solution of infinite one.
Journal ArticleDOI
The Bethe ansatz for 1D interacting anyons
TL;DR: In this article, a pedagogic derivation of the Bethe ansatz solution for 1D interacting anyons is given, which includes a demonstration of the subtle role of the anyonic phases arising from the commutation relations.
Journal ArticleDOI
Quantum magnetism in strongly interacting one-dimensional spinor Bose systems
A. S. Dehkharghani,Artem G. Volosniev,E. J. Lindgren,Jimmy Rotureau,Christian Forssén,D. V. Fedorov,A. S. Jensen,Nikolaj Thomas Zinner +7 more
TL;DR: In this paper, the authors consider trapped two-component bosons with short-range inter-species interactions much larger than their intra-species interaction and show that they have novel energetic and magnetic properties.
Journal ArticleDOI
Ground-state properties of a one-dimensional system of dipoles
Anton Arkhipov,Grigori E. Astrakharchik,Grigori E. Astrakharchik,Alexander V. Belikov,Yu. E. Lozovik +4 more
TL;DR: In this paper, a 1D Bose system with dipole-dipole repulsion was studied at zero temperature by means of a quantum Monte Carlo method, and it was shown that, in the limit of small linear density, the bosonic system of dipole moments acquires many properties of a system of noninteracting fermions.
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Thermalization of a Trapped One-Dimensional Bose Gas via Diffusion.
TL;DR: It is shown that whenever the underlying integrability of the gas is broken by the presence of the external potential, the inevitable diffusive rearrangements between the quasiparticles, quantified by the diffusion constants of theGas, eventually lead the system to thermalize at late times.
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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