Incorporate interference corrections into hydrodynamics and assess a generalized GHD for defects

Develop a systematic hydrodynamic description for the one-dimensional hard-core boson (equivalently free-fermion) gas with two conformal defects that incorporates quantum-interference corrections from multiple reflections, and determine whether a generalized formulation of Generalized Hydrodynamics (GHD) can be constructed to account for these interference effects.

Background

The paper shows that for a domain-wall melting in a free-fermion (hard-core boson) chain with two conformal defects, standard Euler-scale hydrodynamics fails because repeated reflections between defects generate coherent interference effects visible even in the density profile.

Using exact fermionic propagators, the authors derive closed analytic expressions for the dynamics and interpret them semiclassically as sums over interfering classical paths. This motivates the need for a hydrodynamic framework that goes beyond the usual, classical quasi-particle picture to systematically include interference, potentially via a generalized GHD formulation.