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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Excitation spectrum of the Toda lattice for finite temperatures
P. Gruner-Bauer,Franz G. Mertens +1 more
TL;DR: For the Toda lattice, the integral equations of Yang and Yang are derived for the classical limit and their analytical solutions are given in this article, where a finite temperature excitation spectrum of classical solitons and semiclassical phonons are tested by a comparison of the group velocities for vanishing momentum with the sound velocity which can be calculated directly from the thermodynamics.
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Many-body solitonlike states of the bosonic ideal gas
TL;DR: In this article, the authors compare mean-field solitons with the yrast states, being the many-body Lieb-Liniger eigenstates, and show that even in the limit of vanishing interaction, the Yrast states possess features typical for soliton, like phase jumps and density notches.
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Quantum fluctuation effects on the quench dynamics of thermal quasicondensates
Tomasz Świsłocki,Piotr Deuar +1 more
TL;DR: In this article, the influence of quantum fluctuations on the phase, density, and pair correlations in a trapped quasicondensate after a quench of the interaction strength was studied.
Journal ArticleDOI
Integrable spin chains and cellular automata with medium-range interaction
Tamás Gombor,Balázs Pozsgay +1 more
TL;DR: In this paper, integrable spin chains and quantum and classical cellular automata with interaction range ≥ 3 were studied and a general algebraic framework for such models was developed, which leads to a new integrability condition for medium range Hamiltonians.
Journal ArticleDOI
Rise and Fall of a Bright Soliton in an Optical Lattice.
TL;DR: An ultracold atomic gas with attractive interactions in a one-dimensional optical lattice is studied, finding that its excitation spectrum displays a quantum soliton band, corresponding to N-particle bound states, and a continuum band of other, mostly extended, states.
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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