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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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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Replica approach to the KPZ equation with the half Brownian motion initial condition
TL;DR: In this article, the authors considered the one-dimensional Kardar-parisi-Zhang (KPZ) equation with the half Brownian motion initial condition, and employed the replica Bethe ansatz and showed that the generating function of the exponential moments of the height is expressed as a Fredholm determinant.
Journal ArticleDOI
Exact decay and tunnelling dynamics of interacting few-boson systems
TL;DR: In this paper, a wave function-based nonescape probability of finding the full many-body quantum system in the desired region of the total space, rather than (as given in equation (8) of their paper) the density-based NN probability, was used.
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Generalized-Hydrodynamic approach to Inhomogeneous Quenches: Correlations, Entanglement and Quantum Effects
TL;DR: In this paper, a pedagogical introduction to the generalized hydrodynamic approach to inhomogeneous quenches in integrable many-body quantum systems is given, focusing in particular on two classes of problems: bipartitioning protocols and trap quench, which represent two prototypical examples of broken translational symmetry.
Journal ArticleDOI
Introduction to the thermodynamic Bethe ansatz
TL;DR: In this paper, a pedagogical introduction to the thermodynamic Bethe ansatz, a method that allows us to describe the thermodynamics of integrable models whose spectrum is found via the (asymptotic) Bethe Ansatz, is given.
Journal ArticleDOI
On form factors in nested Bethe Ansatz systems
Abstract: We investigate form factors of local operators in a multi-component quantum nonlinear Schrodinger model, a prototype theory solvable by the so-called nested Bethe Ansatz. We determine the analytic properties of the infinite volume form factors using the coordinate Bethe Ansatz solution and establish a connection with the finite volume matrix elements. In the two-component models we derive a set of recursion relations for the 'magnonic form factors', which are the matrix elements on the nested Bethe Ansatz states. In certain simple cases (involving states with only one spin-impurity), we obtain explicit solutions for the recursion relations.
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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