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      Exact large-scale correlations in integrable systems out of equilibrium

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      SciPost Physics
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          Abstract

          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 analyse correlations in the partitioning protocol, extract large-time asymptotics, and, in free models, derive all Euler-scale n -point functions.

          Most cited references84

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          Thermodynamics of a One‐Dimensional System of Bosons with Repulsive Delta‐Function Interaction

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            Quantum Inverse Scattering Method and Correlation Functions

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              Large Scale Dynamics of Interacting Particles

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                Author and article information

                Journal
                SciPost Physics
                SciPost Phys.
                Stichting SciPost
                2018
                November 28 2018
                : 5
                : 5
                Affiliations
                [1 ]King's College London
                Article
                10.21468/SciPostPhys.5.5.054
                8c60236a-ae68-4e83-bf87-045065bd2e12
                © 2018

                Free to read

                https://creativecommons.org/licenses/by/4.0

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