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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Journal ArticleDOI
Tunnelling of narrow Gaussian packets through delta potentials
M A Andreata,V. V. Dodonov +1 more
TL;DR: In this paper, the authors considered transmission and reflection of narrow Gaussian wave packets by delta potentials in the cases of constant and specific (inverse linear) time-dependent strength.
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Large deviations for the Kardar- Parisi-Zhang equation from the Kadomtsev-Petviashvili equation
Journal ArticleDOI
Theory of superfluidity and drag force in the one-dimensional Bose gas
TL;DR: In this paper, the drag force obtained from linear response theory in relation to Landau's criterion of superfluidity is discussed in relation with Anderson localization and the predicted superfluid-insulator transition in these systems.
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Graphene: materials in the flatland
TL;DR: The Wikipedia is a goldmine of information; not just for its many readers, but also for the growing community of researchers who recognize it as a resource of exceptional scale and utility as mentioned in this paper.
Book
Correlations in Low-Dimensional Quantum Gases
TL;DR: In particular, the realisation of pieges hautement anisotropes permet de confiner ces gaz en basse dimension, ou le role des fluctuations quantiques est accru as mentioned in this paper.
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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