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
More filters
Journal ArticleDOI
Three-body repulsive forces among identical bosons in one dimension
TL;DR: In this paper, it was shown that the leading-order correction to the ground-state energy for more than two bosons is accurately described by the lowest-order three-body force in effective field theory that arises due to the off-shell structure of the two-body interaction.
Journal ArticleDOI
The nested SU(N) off-shell Bethe ansatz and exact form factors
TL;DR: In this paper, the form factor equations are solved for an SU(N) invariant S-matrix under the assumption that the antiparticle is identified with the bound state of N-1 particles.
Journal ArticleDOI
Exact correlations in the Lieb-Liniger model and detailed balance out-of-equilibrium
Jacopo De Nardis,Miłosz Panfil +1 more
TL;DR: In this article, the density-density correlation function of the 1D Lieb-Liniger model was studied and an exact expression for the small momentum limit of the static correlator in the thermodynamic limit was obtained.
Transfer matrices and excitations with matrix product states
Zauner,Damian Draxler,Laurens Vanderstraeten,Matthias Degroote,Jutho Haegeman,Marek M. Rams,Stojevic,Norbert Schuch,Frank Verstraete +8 more
Journal ArticleDOI
Quench action and large deviations: Work statistics in the one-dimensional Bose gas.
TL;DR: It is shown that fluctuations close to the mean value of the work exhibit a marked non-Gaussian behavior, even though their probability is always exponentially suppressed below it as L increases, and this approach can be straightforwardly generalized to quantum quenches in other interacting integrable systems.
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