# SciPost Commentary Page

### Original publication:

 Title: Dynamics of the attractive 1D Bose gas: analytical treatment from integrability Author(s): Pasquale Calabrese, Jean-Sébastien Caux As Contributors: Pasquale Calabrese · Jean-Sébastien Caux Journal ref.: J. Stat. Mech.: Th. Exp 2007, P08032 DOI: http://dx.doi.org/10.1088/1742-5468/2007/08/P08032 Date: 2007-08-28

### Abstract:

The physics of the attractive one-dimensional Bose gas (Lieb–Liniger model) is investigated with techniques based on the integrability of the system. Combining a knowledge of particle quasi-momenta to exponential precision in the system size with determinant representations of matrix elements of local operators coming from the algebraic Bethe ansatz, we obtain rather general analytical results for the zero-temperature dynamical correlation functions of the density and field operators. Our results thus provide quantitative predictions for possible future experiments in atomic gases or optical waveguides.

A small correction on this paper concerns the 1/N expansion of the static structure factor in equation (61). Namely, the expression in the current paper contains subleading corrections coming only from the N-1:1 class of states as per equation (64), and did not include the subleading corrections from the class N states (namely the 1/N corrections to equation (62)). The correct form for the static structure factor including also this subleading correction was provided in Y. Castin Eur. Phys. J. B 68, 317–328 (2009) (see its commentary page $\href{/commentary/10.1140/epjb/e2008-00407-3}{\text{here}}$).