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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Nonlocal quantum superpositions of bright matter-wave solitons and dimers
TL;DR: In this article, the scattering of bright quantum solitons at barrier potentials in one-dimensional geometries is investigated and the signatures of the coherent superposition states in an interferometric setup are investigated.
Journal ArticleDOI
State engineering of impurities in a lattice by coupling to a Bose gas
Kevin Keiler,Peter Schmelcher +1 more
TL;DR: In this paper, the authors investigate the localization pattern of interacting impurities, which are trapped in a lattice potential and couple to a Bose gas, and find that the impurities localize either pairwise or completely in a single well.
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One-particle density matrix of trapped one-dimensional impenetrable bosons from conformal invariance
Yannis Brun,Jérôme Dubail +1 more
TL;DR: The one-particle density matrix of the one-dimensional Tonks-Girardeau gas with inhomogeneous density profile is calculated in this paper, thanks to a recent observation that relates this system to a two-dimensional conformal field theory in curved space.
Journal ArticleDOI
Thermodynamic identities and particle number fluctuations in weakly interacting Bose-Einstein condensates
TL;DR: In this article, the authors derived exact thermodynamic identities relating the average number of condensed atoms and the root-mean-square fluctuations determined in different statistical ensembles for the weakly interacting Bose gas confined in a box.
Journal ArticleDOI
Exact solution of a quantized LC circuit coupled to a power source
TL;DR: In this paper, the exact quantum mechanical solution of two-dimensional mesoscopic circuits coupled via inductance is derived by means of a two-step unitary transformation, and the wavefunction, propagator and expectation value of Hamiltonian are evaluated.
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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