Journal ArticleDOI
Exact analysis of an interacting bose gas. i. the general solution and the ground state
Elliott H. Lieb,Werner Liniger +1 more
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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Journal ArticleDOI
Correlation functions of the XXZ Heisenberg spin-1/2 chain in a magnetic field
TL;DR: Using the algebraic Bethe ansatz method and the solution of the quantum inverse scattering problem for local spins, this article obtained multiple integral representations of the $n$-point correlation functions of the XXZ Heisenberg spin-$1 \over 2$ chain in a constant magnetic field.
Journal ArticleDOI
Replica Bethe ansatz studies of two-dimensional interfaces with quenched random impurities
TL;DR: In this paper, the statistical mechanics of interfaces subject to quenched impurities are studied in two dimensions, and the presence of randomness changes the scaling of domain wall fluctuations, and modifies critical behavior at interface-driven depinning (wetting), and commensurate-to-incommensurate phase transitions.
Journal ArticleDOI
Momentum Distribution in the Ground State of the One-Dimensional System of Impenetrable Bosons
TL;DR: In this paper, a mathematically rigorous analysis leading to the determination of major features of the momentum distribution in the limit of an infinitely large system is given, starting with Girardeau's exact analytical formula.
Journal ArticleDOI
Quasilocal charges in integrable lattice systems
TL;DR: In this article, the concept of quasilocal conserved quantities has been studied in integrable quantum lattice systems, and two systematic procedures to rigorously construct families of conserved operators based on quantum transfer matrices are outlined, specializing on anisotropic Heisenberg XXZ spin 1/2 chain.
Journal ArticleDOI
Integral Formulas for the Asymmetric Simple Exclusion Process
Craig A. Tracy,Harold Widom +1 more
TL;DR: In this article, the authors obtained general integral formulas for probabilities in the asymmetric simple exclusion process (ASEP) on the integer lattice with nearest neighbor hopping rates p to the right and q = 1−p to the left.
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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Atomic Scattering in the Presence of an External Confinement and a Gas of Impenetrable Bosons
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