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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The Average Field Approximation for Almost Bosonix Extended Anyons
TL;DR: In this paper, the authors studied the ground state of a large number of 2D anyons in a scaling limit where the statistics parameter is proportional to the inverse of the number of anyons.
Journal ArticleDOI
Bethe Ansatz for the Toda lattice: ground state and excitations
TL;DR: For a one-dimensional chain with exponential plus linear interactions the asymptotic wave functions are constructed by Bethe's ansatz using the exact two-body phase shift as mentioned in this paper.
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 delta-interactions, and prove discreteness of spectra and Weyl laws for the asymptotic eigenvalue counts.
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Field theory of disordered systems -- Avalanches of an elastic interface in a random medium
TL;DR: In this article, a model of a particle in a Brownian random force landscape, applicable to high-dimensional interfaces, is presented, where the interface moves in avalanches, triggered at random points in time, separated by long periods of quiescence.
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Conservation laws for the nonlinear Schrödinger equation
Eugene Gutkin,Eugene Gutkin +1 more
TL;DR: In this paper, a method of calculating the operator densities h ˆ n n = 0, 1, 1, … of the conservation laws for the quantum nonlinear Schrodinger equation was proposed.
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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