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
Citations
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Relaxation dynamics of local observables in integrable systems
TL;DR: In this article, the generalized single-particle overlap coefficient (SPC) was used to estimate the post-quench time evolution of an integrable system in the thermodynamic limit.
Journal ArticleDOI
Zamolodchikov-Faddeev Algebra and Quantum Quenches in Integrable Field Theories
TL;DR: In this paper, the Bogoliubov transformations hold only in the case of quantum quenches in free theories and not in the most general case of interacting theories, and the transformations associated with a change of the interaction in the Sinh-Gordon and the Lieb-Liniger model.
Journal ArticleDOI
Inactive dynamical phase of a symmetric exclusion process on a ring
TL;DR: In this article, the authors investigate the dynamic inactive phase of a simple symmetric exclusion process on a ring and find that as the system's activity is tuned to a lower than average value, the particles progressively lump into a single cluster, thereby forming a kink in the density profile.
Journal ArticleDOI
Exact Liouvillian Spectrum of a One-Dimensional Dissipative Hubbard Model.
TL;DR: This work obtains an exact eigenspectrum of a Liouvillian superoperator by employing a non-Hermitian extension of the Bethe-ansatz method and presents a new class of exactly solvable Liouvillians of open quantum many-body systems, which can be tested with ultracold atoms subject to inelastic collisions.
Journal ArticleDOI
Stationary correlations for the 1D KPZ equation
TL;DR: In this paper, the exact stationary properties of the one-dimensional Kardar-Parisi-Zhang (KPZ) equation were studied by using the replica approach, where the stationary state for the KPZ equation was realized by setting the initial condition the two-sided Brownian motion (BM) with respect to the space variable.
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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