Analogous Hawking Effect: S-Matrix and Thermofield Dynamics

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

Automated summary

We investigate the scattering S-matrix in dispersive media, which gives rise to analogous Hawking radiation. We demonstrate the general structure of scattering under the weak dispersion approximation and discuss potential differences in the production rates of Hawking particles and their antiparticles. Additionally, we parameterize the S-matrix and explore its perturbative structure, connecting it with the thermofield dynamics framework. We find that the thermofield dynamics picture is applicable and naturally leads to a duplication of degrees of freedom, similar to the astrophysical black hole case. Furthermore, we demonstrate the identification of particles on the thermal vacuum with real particles appearing in the scattering.