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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First-principles quantum simulations of many-mode open interacting Bose gases using stochastic gauge methods
TL;DR: In this paper, the quantum dynamics and grand canonical thermodynamics of many-mode (one-, two-, and three-dimensional) interacting Bose gases are simulated from first principles, using a lattice Hamiltonian based on a second-quantized model with two-particle interactions, external potential, and interactions with an environment, with no further approximations.
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Classification of three-state Hamiltonians solvable by Coordinate Bethe Ansatz
TL;DR: In this article, the authors classify all Hamiltonians with rank 1 symmetry, acting on a periodic three-state spin chain, and solve all these Hamiltonians using CBA, and provide their spectrum, eigenfunctions and Bethe equations.
Journal ArticleDOI
Exactly solvable models of quantum nonlinear optics
N. M. Bogoliubov,P. P. Kulish +1 more
TL;DR: There are many models in quantum nonlinear optics that are exactly solvable and allow one to describe physical phenomena beyond perturbation theory as discussed by the authors, and many such models can be solved in the framework of the quantum inverse scattering method.
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Quantum field tomography
TL;DR: In this paper, the authors introduce the concept of quantum field tomography, the efficient and reliable reconstruction of unknown quantum fields based on data of correlation functions, and exemplify the functioning of the approach by reconstructing randomized cMPS from their correlation data and study the robustness of the reconstruction for different noise models.
Journal ArticleDOI
Anomalous frequency shifts in a one-dimensional trapped Bose gas
TL;DR: In this paper, the authors consider a system of interacting bosons in one dimension at a two-body resonance and evaluate the shifts in the frequency of the lowest compressional mode with respect to the dipole mode and find that the effect of the anomaly is to increase the mode's frequency.
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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