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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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Nobel Lecture: Graphene: Materials in the Flatland
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Synthesis and characterization of chiral mesoporous silica
TL;DR: These findings could lead to new uses for mesoporous silica and other chiral pore materials in, for example, catalysis and separation media, where both shape selectivity and enantioselectivity can be applied to the manufacturing of enantiomerically pure chemicals and pharmaceuticals.
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The kardar-parisi-zhang equation and universality class
TL;DR: In this article, the authors present a survey of the development of the Kardar-Parisi-Zhang (KPZ) universality class and its application to a wide class of physical and probabilistic models.
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Study of Exactly Soluble One-Dimensional N-Body Problems
TL;DR: In this article, it was shown that the stationary state solution of the scattering of the three particles is analogous to an electro-magnetic diffraction problem which has already been solved.
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Probability distribution of the free energy of the continuum directed random polymer in 1 + 1 dimensions
TL;DR: In this paper, the authors considered the solution of the stochastic heat equation @TZ D 1 @ 2 X ZZ P W with delta function initial condition Z and obtained explicit formulas for the one-dimensional marginal distributions, the crossover distributions, which interpolate between a standard Gaussian dis- tribution (small time) and the GUE Tracy-Widom distribution (large time).
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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