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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The entanglement entropy of one-dimensional systems in continuous and homogeneous space
TL;DR: In this article, the bipartite entanglement entropy of a compact spatial subsystem in a one-dimensional quantum gas which can be mapped into a non-interacting fermion system is calculated.
Journal ArticleDOI
On the construction of möller operators for the nonlinear schrödinger equation
TL;DR: In this article, the inverse mapping for the quantized theory is obtained with the help of the Merchenko equation, which is the same as in this paper, but with a different operator.
Journal ArticleDOI
Relaxation dynamics of local observables in integrable systems
TL;DR: In this paper, the generalized single-particle overlap coefficient s 0 ψ (λ) is derived from the thermodynamically leading part of the overlaps between the eigenstates of the model and the initial state.
Journal ArticleDOI
Discrete Time q-TASEPs
TL;DR: In this paper, Bernoulli discrete-time q-TASEP is studied and the conditions for the marginal distribution of the location of any given particle are derived for q-deformed versions of the quantum delta Bose gas.
Journal ArticleDOI
Replica Bethe ansatz derivation of the Tracy-Widom distribution of the free energy fluctuations in one-dimensional directed polymers
TL;DR: In this paper, the distribution function of the free energy fluctuations in one-dimensional directed polymers with δ-correlated random potential is studied by mapping the replicated problem to the $N$-particle quantum boson system with attractive interactions.
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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