2017/11/30 by Benjamin Doyon · 1 citation
Physics and Astronomy · Mathematics · #math-ph #cond-mat.stat-mech #hep-th #math.MP
paper · pdf · doi:10.21468/scipostphys.5.5.054
published as SciPost Phys. 5, 054 (2018) · 53 pages, 1 figure. v2: 58 pages, explicit results of two-point functions in sinh-Gordon and Lieb-Liniger model added. v3: 60 pages, minor corrections. v4: 61 pages, one un-necessary assumption taken away, and elements of discussion added in conclusion
arxiv created 2018/10/30 · arxiv updated 2018/11/28
Using the theory of generalized hydrodynamics (GHD), we derive exact Euler-scale dynamical two-point correlation functions of conserved densities and currents in inhomogeneous, non-stationary states of many-body integrable systems with weak space-time variations. This extends previous works to inhomogeneous and non-stationary situations. Using GHD projection operators, we further derive formulae for Euler-scale two-point functions of arbitrary local fields, purely from the data of their homogeneous one-point functions. These are new also in homogeneous generalized Gibbs ensembles. The technique is based on combining a fluctuation-dissipation principle along with the exact solution by characteristics of GHD, and gives a recursive procedure able to generate n-point correlation functions. Owing to the universality of GHD, the results are expected to apply to quantum and classical integrable field theory such as the sinh-Gordon model and the Lieb-Liniger model, spin chains such as the XXZ and Hubbard models, and solvable classical gases such as the hard rod gas and soliton gases. In particular, we find Leclair-Mussardo-type infinite form-factor series in integrable quantum field theory, and exact Euler-scale two-point functions of exponential fields in the sinh-Gordon model and of powers of the density field in the Lieb-Liniger model. We also analyze correlations in the partitioning protocol, extract large-time asymptotics, and, in free models, derive all Euler-scale n-point functions.