Quantum electron self-interaction in a strong laser field

The quantum state of an electron in a strong laser field is altered if the interaction of the electron with its own electromagnetic field is taken into account. Starting from the Schwinger-Dirac equation, we determine the states of an electron in a plane-wave field with inclusion, at leading order, of its electromagnetic self-interaction. On the one hand, the electron states show a pure "quantum" contribution to the electron quasi-momentum, conceptually different from the conventional "classical" one arising from the quiver motion of the electron. On the other hand, the electron self-interaction induces a distinct dynamics of the electron spin, whose effects are shown to be measurable in principle with available technology.Comment: 5 pages, 2 figure

Slow energy relaxation and localization in 1D lattices

We investigate the energy relaxation process produced by thermal baths at zero temperature acting on the boundary atoms of chains of classical anharmonic oscillators. Time-dependent perturbation theory allows us to obtain an explicit solution of the harmonic problem: even in such a simple system nontrivial features emerge from the interplay of the different decay rates of Fourier modes. In particular, a crossover from an exponential to an inverse-square-root law occurs on a time scale proportional to the system size $N$. A further crossover back to an exponential law is observed only at much longer times (of the order $N^3$). In the nonlinear chain, the relaxation process is initially equivalent to the harmonic case over a wide time span, as illustrated by simulations of the $\beta$ Fermi-Pasta-Ulam model. The distinctive feature is that the second crossover is not observed due to the spontaneous appearance of breathers, i.e. space-localized time-periodic solutions, that keep a finite residual energy in the lattice. We discuss the mechanism yielding such solutions and also explain why it crucially depends on the boundary conditions.Comment: 16 pages, 6 figure

Cooling nonlinear lattices toward localisation

We describe the energy relaxation process produced by surface damping on lattices of classical anharmonic oscillators. Spontaneous emergence of localised vibrations dramatically slows down dissipation and gives rise to quasi-stationary states where energy is trapped in the form of a gas of weakly interacting discrete breathers. In one dimension (1D), strong enough on--site coupling may yield stretched--exponential relaxation which is reminiscent of glassy dynamics. We illustrate the mechanism generating localised structures and discuss the crucial role of the boundary conditions. For two--dimensional (2D) lattices, the existence of a gap in the breather spectrum causes the localisation process to become activated. A statistical analysis of the resulting quasi-stationary state through the distribution of breathers' energies yield information on their effective interactions.Comment: 10 pages, 11 figure

Gauss-Codazzi thermodynamics on the timelike screen

It is a known result by Jacobson that the flux of energy-matter through a local Rindler horizon is related with the expansion of the null generators in a way that mirrors the first law of thermodynamics. We extend such a result to a timelike screen of observers with finite acceleration. Since timelike curves have more freedom than null geodesics, the construction is more involved than Jacobson's and few geometrical constraints need to be imposed: the observers' acceleration has to be constant in time and everywhere orthogonal to the screen. Moreover, at any given time, the extrinsic curvature of the screen has to be flat. The latter requirement can be weakened by asking that the extrinsic curvature, if present at the beginning, evolves in time like on a cone and just rescales proportionally to the expansion.Comment: 8+1 pages, final versio

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

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

Improved local-constant-field approximation for strong-field QED codes

The local-constant-field approximation (LCFA) is an essential theoretical tool for investigating strong-field QED phenomena in background electromagnetic fields with complex spacetime structure. In our previous work [Phys.~Rev.~A~\textbf{98}, 012134 (2018)] we have analyzed the shortcomings of the LCFA in nonlinear Compton scattering at low emitted photon energies for the case of a background plane-wave field. Here, we generalize that analysis to background fields, which can feature a virtually arbitrary spacetime structure. In addition, we provide an explicit and simple implementation of an improved expression of the nonlinear Compton scattering differential probability that solves the main shortcomings of the standard LCFA in the infrared region, and is suitable for background electromagnetic fields with arbitrary spacetime structure such as those occurring in particle-in-cell simulations. Finally, we carry out a systematic procedure to calculate the probability of nonlinear Compton scattering per unit of emitted photon light-cone energy and of nonlinear Breit-Wheeler pair production per unit of produced positron light-cone energy beyond the LCFA in a plane-wave background field, which allows us to identify the limits of validity of this approximation quantitatively.Comment: 15 pages, 3 figure

Entre théorie et pratique. Aristote et le strabisme de la techne

The Aristotelian reflection on the epistemological status of techne, and more specifically on the definition of rhetoric as a techne, can help us to rethink the very actual cleavage between theory and practice. A good techne, as the rhetoric has to be according to Aristotle, has not to choose between theory and practice, between the universal and the particular, but should be able to look simultaneously in both directions and to keep them together. We will try to show that may be worth to rediscover and to introduce the Aristotelian notion of techne into the contemporary epistemological and philosophical debate

The IR-Completion of Gravity: What happens at Hubble Scales?

We have recently proposed an "Ultra-Strong" version of the Equivalence Principle (EP) that is not satisfied by standard semiclassical gravity. In the theory that we are conjecturing, the vacuum expectation value of the (bare) energy momentum tensor is exactly the same as in flat space: quartically divergent with the cut-off and with no spacetime dependent (subleading) ter ms. The presence of such terms seems in fact related to some known difficulties, such as the black hole information loss and the cosmological constant problem. Since the terms that we want to get rid of are subleading in the high-momentum expansion, we attempt to explore the conjectured theory by "IR-completing" GR. We consider a scalar field in a flat FRW Universe and isolate the first IR-correction to its Fourier modes operators that kills the quadratic (next to leading) time dependent divergence of the stress energy tensor VEV. Analogously to other modifications of field operators that have been proposed in the literature (typically in the UV), the present approach seems to suggest a breakdown (here, in the IR, at large distances) of the metric manifold description. We show that corrections to GR are in fact very tiny, become effective at distances comparable to the inverse curvature and do not contain any adjustable parameter. Finally, we derive some cosmological implications. By studying the consistency of the canonical commutation relations, we infer a correction to the distance between two comoving observers, which grows as the scale factor only when small compared to the Hubble length, but gets relevant corrections otherwise. The corrections to cosmological distance measures are also calculable and, for a spatially flat matter dominated Universe, go in the direction of an effective positive acceleration.Comment: 27 pages, 2 figures. Final version, references adde