Spectral boundary conditions and solitonic solutions in a classical Sellmeier dielectric

Electromagnetic field interactions in a dielectric medium represent a longstanding field of investigation, both at the classical level and at the quantum one. We propose a 1+1 dimensional toy-model which consists of an half-line filling dielectric medium, with the aim to set up a simplified situation where technicalities related to gauge invariance and, as a consequence, physics of constrained systems are avoided, and still interesting features appear. In particular, we simulate the electromagnetic field and the polarization field by means of two coupled scalar fields $\phi$,$\psi$ respectively, in a Hopfield-like model. We find that, in order to obtain a physically meaningful behaviour for the model, one has to introduce spectral boundary conditions depending on the particle spectrum one is dealing with. This is the first interesting achievement of our analysis. The second relevant achievement is that, by introducing a nonlinear contribution in the polarization field $\psi$, with the aim of mimicking a third order nonlinearity in a nonlinear dielectric, we obtain solitonic solutions in the Hopfield model framework, whose classical behaviour is analyzed too.Comment: 12 pages, 1 figur

Pair-production of charged Dirac particles on charged Nariai and ultracold black hole manifolds

Spontaneous loss of charge by charged black holes by means of pair-creation of charged Dirac particles is considered. We provide three examples of exact calculations for the spontaneous discharge process for 4D charged black holes by considering the process on three special non-rotating de Sitter black hole backgrounds, which allow to bring back the problem to a Kaluza-Klein reduction. Both the zeta-function approach and the transmission coefficient approach are taken into account. A comparison between the two methods is also provided, as well as a comparison with WKB results. In the case of non-zero temperature of the geometric background, we also discuss thermal effects on the discharge process.Comment: 27 page

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

Phi-Psi model for Electrodynamics in dielectric media: exact quantisation in the Heisenberg representation

We investigate the quantization in the Heisenberg representation of a model which represents a simplification of the Hopfield model for dielectric media, where the electromagnetic field is replaced by a scalar field $\phi$ and the role of the polarization field is played by a further scalar field $\psi$. The model, which is quadratic in the fields, is still characterized by a nontrivial physical content, as the physical particles correspond to the polaritons of the standard Hopfield model of condensed matter physics. Causality is also taken into account and a discussion of the standard interaction representation is also considered.Comment: 9 page

Exact quantisation of the relativistic Hopfield model

We investigate the quantisation in the Heisenberg representation of a relativistically covariant version of the Hopfield model for dielectric media, which entails the interaction of the quantum electromagnetic field with the matter dipole fields. The matter fields are represented by a mesoscopic polarization field. A full quantisation of the model is provided in a covariant gauge, with the aim of maintaining explicit relativistic covariance. Breaking of the Lorentz invariance due to the intrinsic presence in the model of a preferred reference frame is also taken into account. Relativistic covariance forces us to deal with the unphysical (scalar and longitudinal) components of the fields, furthermore it introduces, in a more tricky form, the well-known dipole ghost of standard QED in a covariant gauge. In order to correctly dispose of this contribution, we implement a generalized Lautrup trick. Furthermore, causality and the relation of the model with the Wightman axioms are also discussed.Comment: 24 page

Path integral quantization of the relativistic Hopfield model

The path integral quantization method is applied to a relativistically covariant version of the Hopfield model, which represents a very interesting mesoscopic framework for the description of the interaction between quantum light and dielectric quantum matter, with particular reference to the context of analogue gravity. In order to take into account the constraints occurring in the model, we adopt the Faddeev-Jackiw approach to constrained quantization in the path integral formalism. In particular we demonstrate that the propagator obtained with the Faddeev-Jackiw approach is equivalent to the one which, in the framework of Dirac canonical quantization for constrained systems, can be directly computed as the vacuum expectation value of the time ordered product of the fields. Our analysis also provides an explicit example of quantization of the electromagnetic field in a covariant gauge and coupled with the polarization field, which is a novel contribution to the literature on the Faddeev-Jackiw procedure.Comment: 16 page

The Hawking effect in dielectric media and the Hopfield model

We consider the so-called Hopfield model for the electromagnetic field in a dielectric dispersive medium in a framework in which one allows a space-time dependence of microscopic parameters, aimed to a phenomenological description of a space-time varying dielectric perturbation induced by means of the Kerr effect. We discuss the analogue Hawking effect, by first analyzing the geometrical optics for the Hopfield model, and then by introducing a simplified model which has the bonus to avoid many difficulties which are involved in the full Hopfield model, still keeping the same dispersion relation. Amplitude calculations are indicated, and generalized Manley-Rowe identities are derived in a quantum scattering theory framework. Our main result is an analytical calculation of the spontaneous thermal emission in the single-branch case, which is provided non perturbatively for the first time in the framework of dielectric black holes. An universal mechanism for thermality between optical black holes and acoustic black holes is also pointed out.Comment: 21 pages and 3 figures, improvements adde

The Hopfield model revisited: Covariance and Quantization

There are several possible applications of quantum electrodynamics in dielectric media which require a quantum description for the electromagnetic field interacting with matter fields. The associated quantum models can refer to macroscopic electromagnetic fields or, in alternative, to mesoscopic fields (polarization fields) describing an effective interaction between electromagnetic field and matter fields. We adopt the latter approach, and focus on the Hopfield model for the electromagnetic field in a dielectric dispersive medium in a framework in which space-time dependent mesoscopic parameters occur, like susceptibility, matter resonance frequency, and also coupling between electromagnetic field and polarization field. Our most direct goal is to describe in a phenomenological way a space-time varying dielectric perturbation induced by means of the Kerr effect in nonlinear dielectric media. This extension of the model is implemented by means of a Lorentz-invariant Lagrangian which, for constant microscopic parameters, and in the rest frame, coincides with the standard one. Moreover, we deduce a covariant scalar product and provide a covariant quantization scheme which keeps into account the constraints implicit in the model. Examples of viable applications are indicated.Comment: 14 pages, improvements adde