Journal ArticleDOI
Exact analysis of an interacting bose gas. i. the general solution and the ground state
Elliott H. Lieb,Werner Liniger +1 more
Reads0
Chats0
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
More filters
Journal ArticleDOI
Ultracold Atoms Confined in an Optical Lattice Plus Parabolic Potential: A Closed-Form Approach
TL;DR: In this article, the authors studied the collective oscillations of ideal bosonic and fermionic ensembles induced by small displacements of the parabolic potential, and showed that the non-interacting problem is exactly solvable in terms of Mathieu functions.
Journal ArticleDOI
Basics of Bose-Einstein Condensation
TL;DR: In this paper, a review is devoted to the elucidation of the basic problems arising in the theoretical investigation of systems with Bose-Einstein condensate and its relation to global gauge symmetry breaking.
Journal ArticleDOI
Orthogonality and Completeness of the Bethe Ansatz Eigenstates of the Nonlinear Schroedinger Model
TL;DR: In this paper, a rigorous proof of the orthogonality and completeness of the Bethe Ansatz eigenstates of the N-body Hamiltonian of the nonlinear Schroedinger model on a finite interval is given.
Journal ArticleDOI
Emergence of curved light-cones in a class of inhomogeneous Luttinger liquids
TL;DR: In this article, it was shown that a class of inhomogenous Luttinger liquids (those with a uniform LUTtinger parameter $K$) at low energy display the universal phenomenon of curved light cones: gapless excitations propagate along the geodesics of the metric.
Journal ArticleDOI
Exact methods in analysis of nonequilibrium dynamics of integrable models: application to the study of correlation functions in nonequilibrium 1D Bose gas
TL;DR: In this paper, the form-factor approach was combined with the method of intertwining operator, which allows explicit summation over intermediate states and analysis of the time evolution of non-local density-density correlation functions.
References
More filters
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.
Related Papers (5)
Atomic Scattering in the Presence of an External Confinement and a Gas of Impenetrable Bosons
Maxim Olshanii,Maxim Olshanii +1 more