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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An exact stochastic field method for the interacting Bose gas at thermal equilibrium
Iacopo Carusotto,Yvan Castin +1 more
TL;DR: In this article, Carusotto et al. presented a new exact method to numerically compute the thermodynamical properties of an interacting Bose gas in the canonical ensemble, where the density operator ρ was written as an average of Hartree dyadics and the exact imaginary-time evolution of ρ is recovered after averaging over noise.
Journal ArticleDOI
Two-point generating function of the free energy for a directed polymer in a random medium
Sylvain Prolhac,Herbert Spohn +1 more
TL;DR: In this paper, a 1+1 dimensional directed continuum polymer in a Gaussian delta-correlated space-time random potential was considered and the moments of the partition function were expressed in terms of the attractive delta-Bose gas on the line.
Journal ArticleDOI
Instructive History of the Quantum Inverse Scattering Method
TL;DR: The classical inverse scattering method was invented in course of investigation of the KdV equation [1] and was described in a short and famous now research letter by Gardner, Green, Kruskal and Miura [2] in 1967.
Journal ArticleDOI
Two-time free energy distribution function in (1+1) directed polymers
TL;DR: In this paper, the explicit expression for the two-time free energy distribution function in one-dimensional directed polymers in random potential is derived in terms of the Bethe ansatz replica technique 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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