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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One-particle density matrix of trapped one-dimensional impenetrable bosons from conformal invariance
Yannis Brun,Jérôme Dubail +1 more
TL;DR: The one-particle density matrix of the one-dimensional Tonks-Girardeau gas with inhomogeneous density profile is calculated in this paper, thanks to a recent observation that relates this system to a two-dimensional conformal field theory in curved space.
Posted Content
Discrete time q-TASEPs
TL;DR: In this paper, Bernoulli discrete-time q-TASEP (Q-TAASEP) approximations are obtained for a large class of observables of the system to completely characterize their fixed time distributions when started from step initial condition.
Journal ArticleDOI
Interaction quench in a Lieb-Liniger model and the KPZ equation with flat initial conditions
TL;DR: In this paper, the authors compare their previous exact solution and a new conjecture by De Nardis et al., which leads to new exact results and conjectures for both the quantum quench and the KPZ problem.
Journal ArticleDOI
Center-of-mass motion as a sensitive convergence test for variational multimode quantum dynamics
TL;DR: In this paper, the separable quantum motion of the center of mass can be used to sensitively detect unconverged numerical multiparticle dynamics in harmonic potentials, based on an experimentally relevant example of attractively interacting bosons in one dimension.
Journal ArticleDOI
One-Dimensional Liquid ^{4}He: Dynamical Properties beyond Luttinger-Liquid Theory.
TL;DR: The zero-temperature dynamical structure factor of one-dimensional liquid is computed by means of state-of-the-art quantum Monte Carlo and analytic continuation techniques, and a transition from a highly compressible critical liquid to a quasisolid regime is revealed.
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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