Generalised hydrodynamics of particle creation and decay

Unstable particles rarely feature in conjunction with integrability 1+1D quantum field theory. However, the family of homogenous sine-Gordon models provides a rare example where both stable and unstable bound states are present spectrum whilst scattering matrix is diagonal solves usual bootstrap equations. In standard picture, result from complex poles $S$-matrix located unphysical sheet rapidity space. Since they not part asymptotic spectrum, their presence only felt through effect have on physical quantities associated either to theory as whole (i.e.~scaling functions, correlation functions) or themselves (i.e.~energy/particle density). two recent publications, different out-of-equilibrium settings has been studied. It shown that specific signatures many interest. A good way select those adopt generalised hydrodynamic approach consider effective velocities particle densities For an initial state given by spacial gaussian profile temperatures peaked at origin, time evolution gives rise spectral exhibit hallmarks creation decay particles. While these observed numerically elsewhere, this paper explores quantitative qualitative dependence parameters problem. We also other characterised "inverted gaussian" "double temperature profiles.