Analogous Hawking Effect: S-Matrix and Thermofield Dynamics

We consider the full S-matrix in scattering giving rise to analogous Hawking radiation dispersive media. show general structure of weak dispersion approximation and discuss some unnoticed features primary process, with a possible generalization phenomenology effect. In particular, we stress that particle its antiparticle partner priori could also be produced different rates. provide parameterization S-matrix, adopting Iwasawa decomposition for matrix itself. Then, assume perturbative suitable sense is allowed display corresponding expansion. connection at leading order, thermofield dynamics (TFD) framework TFD picture still available, doubling degrees freedom emerging natural way, as astrophysical black hole case. Furthermore, particles on thermal vacuum can identified real appearing scattering.