Inspired by the condensed matter analogues of black holes (a.k.a. dumb holes), we study Hawking radiation in the presence of a modified dispersion relation which becomes super-luminal at large wave-numbers. In the usual stationary coordinates $(t,x)$
, one can describe the asymptotic evolution of the wave-packets in WKB, but this WKB approximation breaks down in the vicinity of the horizon, thereby allowing for a mixing between initial and final creation and annihilation operators. Thus, one might be tempted to identify this point where WKB breaks down with the moment of particle creation. However, using different coordinates $(tau,U)$, we find that one can evolve the waves so that WKB in these coordinates is valid throughout this transition region -- which contradicts the above identification of the breakdown of WKB as the cause of the radiation. Instead, our analysis suggests that the tearing apart of the waves into two different asymptotic regions (inside and outside the horizon) is the major ingredient of Hawking radiation.
We study electronic transport in graphene under the influence of a transversal magnetic field $f{B}(f{r})=B(x)f{e}_z$ with the asymptotics $B(xtopminfty)=pm B_0$, which could be realized via a folded graphene sheet in a constant magnetic field, for e
xample. By solving the effective Dirac equation, we find robust modes with a finite energy gap which propagate along the fold -- where particles and holes move in opposite directions. Exciting these particle-hole pairs with incident photons would then generate a nearly perfect charge separation and thus a strong magneto-thermoelectric (Nernst-Ettingshausen) or magneto-photoelectric effect -- even at room temperature.
One of the most striking examples for the production of particles out of the quantum vacuum due to external conditions is cosmological particle creation, which is caused by the expansion or contraction of the Universe. Already in 1939, Schrodinger un
derstood that the cosmic evolution could lead to a mixing of positive and negative frequencies and that this would mean production or annihilation of matter, merely by the expansion. Later this phenomenon was derived via more modern techniques of quantum field theory in curved space-times by Parker (who apparently was not aware of Schrodingers work) and subsequently has been studied in numerous publications. Even though cosmological particle creation typically occurs on extremely large length scales, it is one of the very few examples for such fundamental effects where we actually may have observational evidence: According to the inflationary model of cosmology, the seeds for the anisotropies in the cosmic microwave background (CMB) and basically all large scale structures stem from this effect. In this Chapter, we shall provide a brief discussion of this phenomenon and sketch a possibility for an experimental realization via an analogue in the laboratory.
Belgiorno et al have reported on experiments aiming at the detection of (the analogue of) Hawking radiation using laser filaments [F. Belgiorno et al, Phys. Rev. Lett. 105, 203901 (2010)]. They sent intense focused Bessel pulses into a non-linear die
lectric medium in order to change its refractive index via the Kerr effect and saw creation of photons orthogonal to the direction of travel of the pluses. Since the refractive index change in the pulse generated a phase horizon (where the phase velocity of these photons equals the pulse speed), they concluded that they observed the analogue of Hawking radiation. We study this scenario in a model with a phase horizon and a phase velocity very similar to that of their experiment and find that the effective metric does not quite correspond to a black hole. The photons created in this model are not due to the analogue of black hole evaporation but have more similarities to cosmological particle creation. Nevertheless, even this effect cannot explain the observations -- unless the pulse has significant small scale structure in both the longitudinal and transverse dimensions.
Motivated by recent experimental progress to manipulate the refractive index of dielectric materials by strong laser beams, we study some aspects of the quantum radiation created by such refractive index perturbations.
Recently it has been found that the superposition of a strong and slow electric field with a weaker and faster pulse can significantly enhance the probability for non-perturbative electron-positron pair creation out of the vacuum -- the dynamically a
ssisted Sauter-Schwinger effect. Via the WKB method, we estimate the momentum dependence of the pair creation probability and compare it to existing numerical results. Besides the theoretical interest, a better understanding of this pair creation mechanism should be helpful for the planned experiments aiming at its detection.
We study the Mott phase of the Bose-Hubbard model on a tilted lattice. On the (Gutzwiller) mean-field level, the tilt has no effect -- but quantum fluctuations entail particle-hole pair creation via tunneling. For small potential gradients (long-wave
length limit), we derive a quantitative analogy to the Sauter-Schwinger effect, i.e., electron-positron pair creation out of the vacuum by an electric field. For large tilts, we obtain resonant tunneling related to Bloch oscillations.
