Abstract

Hydrodynamics is a powerful framework for large-wavelength phenomena in many-body systems. At its basis is the assumption that one can reduce the dynamics to that of long-lived, effective degrees of freedom obtained from the available conservation laws. This fundamental idea, applied traditionally on systems with few conservation laws, can be extended to integrable systems, which admit an extensive number. The ensuing ``generalised hydrodynamics” (GHD) is a universal theory for the large-scale dynamics in integrable classical and quantum chains, gases and fields. In particular, the GHD equations are equivalent to the kinetic equations found, much earlier, in soliton gases. Until now, in quantum interacting systems the only derivation available is based on the assumption of local generalised thermalisation, with exact expressions of average currents playing a crucial role. By contrast, in soliton gases, the kinetic equations can be derived from an application of Whitham modulation theory. Are there first-principle derivations, or a ``quantum modulation theory”, from which the GHD equations can be obtained without the assumption of local generalised thermalisation? I will propose such derivations, in particular using what can be seen as a simple version of quantum modulation, in a paradigmatic model of quantum integrability, the Lieb-Liniger gas.