Journal ArticleDOI
Exact analysis of an interacting bose gas. i. the general solution and the ground state
Elliott H. Lieb,Werner Liniger +1 more
TLDR
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
Quantum graphs with two-particle contact interactions
Jens Bolte,Joachim Kerner +1 more
TL;DR: In this paper, the authors construct models of many-particle quantum graphs with singular twoparticle contact interactions, which can be either hardcore-or δ-interactions.
Dissertation
Variational renormalization group methods for extended quantum systems
TL;DR: Thesis submitted in fulfillment of the requirements for the degree of Doctor (Ph.D.) in Sciences: Physics as discussed by the authors, was submitted in fulfilment of the requirement of the degree.
Journal ArticleDOI
Resonant tunnelling through short-range singular potentials
TL;DR: In this article, a three-parameter family of point interactions constructed from sequences of symmetric barrier and well-barrier rectangles is studied in the limit, when the rectangles are squeezed to zero width but the barrier height and the well depth become infinite (the zero-range limit).
Journal ArticleDOI
Dark-soliton-like excitations in the Yang-Gaudin gas of attractively interacting fermions
TL;DR: In this article, the yrast states of the balanced spin Fermi gas with attractive delta-function interactions in one dimension with the exactly solvable Yang-Gaudin model were studied.
Journal ArticleDOI
Universal duality transformations in interacting one-dimensional quantum systems
TL;DR: In this article, a general theory of local unitary transformations between one-dimensional quantum systems of bosons and fermions with arbitrary spin or internal structure, single-particle dispersion, and low-energy interactions in the universal regime was developed.
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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Atomic Scattering in the Presence of an External Confinement and a Gas of Impenetrable Bosons
Maxim Olshanii,Maxim Olshanii +1 more