Dynamic and static density-density correlations in the one-dimensional Bose gas: Exact results and approximations

Alexander Yu. Cherny and Joachim Brand
Phys. Rev. A 79, 043607 – Published 10 April 2009

Abstract

We discuss approximate formulas for the dynamic structure factor of the one-dimensional Bose gas in the Lieb-Liniger model that appear to be applicable over a wide range of the relevant parameters such as the interaction strength, frequency, and wave number. The suggested approximations are consistent with the exact results known in limiting cases. In particular, we encompass exact edge exponents as well as the Luttinger-liquid and perturbation theoretic results. We further discuss derived approximations for the static structure factor and the pair distribution function g(x). The approximate expressions show excellent agreement with numerical results based on the algebraic Bethe ansatz.

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  • Received 17 December 2008

DOI:https://doi.org/10.1103/PhysRevA.79.043607

©2009 American Physical Society

Authors & Affiliations

Alexander Yu. Cherny1 and Joachim Brand2

  • 1Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia
  • 2Centre for Theoretical Chemistry and Physics and Institute of Natural Sciences, Massey University, Private Bag 102 904, North Shore, Auckland 0745, New Zealand

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Issue

Vol. 79, Iss. 4 — April 2009

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