Abstract
We review some aspects of our longstanding research concerning the analogous Hawking effect in dispersive dielectric media. We introduce nonlinear contributions in the polarization field in the relativistically covariant version of the Hopfield model and then, in order to provide a simplified description aimed at avoiding some subtleties in the quantization of the original model, we discuss the so-called ϕψ-model. We show that the nonlinearity allows for introducing in a self-consistent way the otherwise phenomenological dependence of the susceptibility and of the resonance frequency ω0 on the spacetime variables, and this is a consequence of the linearization of the model around solitonic solutions representing propagating perturbations of the refractive index, to be then associated with the Hawking effect.
Highlights
Since its theoretical discovery, the Hawking effect [1] has represented a very important topic for theoretical physics
Notwithstanding, an evident drawback emerged: any hope of experimental verification for the Hawking effect received a strong hindrance by the too low temperature which could be associated with astrophysical black holes, as, e.g., in the case of a Sun-mass black hole the predicted temperature for a distant observer would amount to a few tenth of nanoKelvins, and, as such, its measurement would be deeply hindered e.g., by the 2.7 K of the cosmic background radiation
We reviewed and discussed nonlinear contributions in the polarization field in the relativistically covariant version of the Hopfield model and its simplified version represented by the φψ-model
Summary
The Hawking effect [1] has represented a very important topic for theoretical physics. We limit ourselves to point out that this research field is going to become a further very relevant chapter in studies for quantum field theory in condensed matter systems, nowadays more focused on topological effects In this brief review, we summarize some aspects of our longstanding studies aimed at providing an analytical deduction of thermality of the analogue Hawking emission in dielectric media. The Hawking effect in nonlinear dielectric media affected by the Kerr effect is associated with the aforementioned dielectric perturbation propagating in the dielectric medium This moving dielectric perturbation amounts to a traveling perturbation of the refractive index, to which the possibility to generate analogous Hawking radiation is strictly related under suitable conditions allowing the existence of a black hole/white hole horizon (or both) [7,10,11,12,13,14,15,16,17,18,19]. Further steps towards an analytical deduction of the thermality for dielectric black holes in the simplified model are sketched
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