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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Integrable many-body problems and functional equations
TL;DR: In this article, the conditions necessaires for l'integrabilite d'une classe de problemes a n corps quantiques are described, and a set of conditions necessary and sufficient for integration are discussed.
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General finite-size effects for zero-entropy states in one-dimensional quantum integrable models
Sebas Eliens,Jean-Sébastien Caux +1 more
TL;DR: In this article, a general derivation of the spectrum of excitations for gapless states of zero entropy density in Bethe ansatz solvable models is presented, which is valid for an arbitrary choice of bare energy function which is relevant to situations where the Hamiltonians for time evolution differs from the Hamiltonian in a generalized Gibbs ensemble.
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The Physics of Self-Adjoint Extensions: One-Dimensional Scattering Problem for the Coulomb Potential
TL;DR: In this paper, the authors considered a single-center scattering problem on the entire axis with the original potential α|x|−1 and showed that point-like δ-corrections to the potential must necessarily be involved for any choice of the admissible self-adjoint extension.
Time evolution of the xxz heisenberg model
TL;DR: In this article, the authors describe the evolution of the Heisenberg Model in the context of the DISSERTATION Time Evolution of the XXZ Heisenburg Model. But
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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