title: Integral method for the calculation of Hawking radiation in dispersive media. I. Symmetric asymptotics.
abstract: Hawking radiation has become experimentally testable thanks to the many analog systems which mimic the effects of the event horizon on wave propagation. These systems are typically dominated by dispersion and give rise to a numerically soluble and stable ordinary differential equation only if the rest-frame dispersion relation Ω^{2}(k) is a polynomial of relatively low degree. Here we present a new method for the calculation of wave scattering in a one-dimensional medium of arbitrary dispersion. It views the wave equation as an integral equation in Fourier space, which can be solved using standard and efficient numerical techniques.
authors.affiliation: Laboratoire de Physique Théorique, CNRS UMR 8627, Bâtiment 210, Université Paris-Sud 11, 91405 Orsay Cedex, France.
authors.forename: Scott
authors.initials: S
authors.lastname: Robertson
authors.affiliation: Department of the Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel.
authors.forename: Ulf
authors.initials: U
authors.lastname: Leonhardt