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      Diffusion in generalized hydrodynamics and quasiparticle scattering

      1 , 2 , 3
      SciPost Physics
      Stichting SciPost

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          Abstract

          We extend beyond the Euler scales the hydrodynamic theory for quantum and classical integrable models developed in recent years, accounting for diffusive dynamics and local entropy production. We review how the diffusive scale can be reached via a gradient expansion of the expectation values of the conserved fields and how the coefficients of the expansion can be computed via integrated steady-state two-point correlation functions, emphasising that {\mathcal PT} -symmetry can fully fix the inherent ambiguity in the definition of conserved fields at the diffusive scale. We develop a form factor expansion to compute such correlation functions and we show that, while the dynamics at the Euler scale is completely determined by the density of single quasiparticle excitations on top of the local steady state, diffusion is due to scattering processes among quasiparticles, which are only present in truly interacting systems. We then show that only two-quasiparticle scattering processes contribute to the diffusive dynamics. Finally we employ the theory to compute the exact spin diffusion constant of a gapped XXZ spin -1/2 chain at finite temperature and half-filling, where we show that spin transport is purely diffusive.

          Most cited references163

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          Time Dependence of Correlation Functions Following a Quantum Quench

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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
                2542-4653
                2019
                April 25 2019
                : 6
                : 4
                Affiliations
                [1 ]Ghent University
                [2 ]Laboratoire de Physique Théorique
                [3 ]King's College London
                Article
                10.21468/SciPostPhys.6.4.049
                8485b6ba-3c5e-4992-84ea-360c29e730ae
                © 2019

                This work is licensed under a Creative Commons Attribution 4.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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                Physics
                Physics

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