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We study the phonon fluxes emitted when the condensate velocity crosses the speed of sound, i.e., in backgrounds which are analogous to that of a black hole. We focus on elongated one dimensional condensates and on stationary flows. Our theoretical analysis and numerical results are based on the Bogoliubov-de Gennes equation without further approximation. The spectral properties of the fluxes and of the long distance density-density correlations are obtained, both with and without an initial temperature. In realistic conditions, we show that the condensate temperature dominates the fluxes and thus hides the presence of the spontaneous emission (the Hawking effect). We also explain why the temperature amplifies the long distance correlations which are intrinsic to this effect. This confirms that the correlation pattern offers a neat signature of the Hawking effect. Optimal conditions for observing the pattern are discussed, as well as correlation patterns associated with scattering of classical waves. Flows associated with white holes are also considered.

a Data from ref 82. b Data from ref 81f, competition experiment starting from the 2-bromothioether. c Data from ref 83, from k −1 /k H , assuming the rate constant for the reduction of an alkyl radical by an alkanethiol is k H = 10 7 M −1 s −1 . d Data from ref 80. Additional data can be found in refs 27, 78, 84.

In a recent work, Unruh showed that Hawking radiation is unaffected by a truncation of free field theory at the Planck scale. His analysis was performed numerically and based on a hydrodynamical model. In this work, by analytical methods, the mathematical and physical origin of Unruh's result is revealed. An alternative truncation scheme which may be more appropriate for black hole physics is proposed and analyzed. In both schemes the thermal Hawking radiation remains unaffected even though transplanckian energies no longer appear. The universality of this result is explained by working in momentum space. In that representation, in the presence of a horizon, the d'Alembertian equation becomes a singular first order equation. In addition, the boundary conditions corresponding to vacuum before the black hole formed are that the in-modes contain positive momenta only. Both properties remain valid when the spectrum is truncated and they suffice to obtain Hawking radiation.2

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We study the fluxes emitted by black holes when using dispersive field theories. We work with stationary one-dimensional backgrounds which are asymptotically flat on both sides of the horizon. The asymptotic fluxes are governed by a 3 Â 3 Bogoliubov transformation. The fluxes emitted by the corresponding white holes are regular and governed by the inverse transformation. We numerically compute the spectral properties of these fluxes for both sub-and superluminal quartic dispersion. The leading deviations with respect to the dispersionless flux are computed and shown to be governed by a critical frequency above which there is no radiation. Unlike the UV scale governing dispersion, its value critically depends on the asymptotic properties of the background. We also study the flux outside the robust regime. In particular we show that its low-frequency part remains almost thermal but with a temperature which significantly differs from the standard one. Applications to four-dimensional black holes and Bose-Einstein condensates are in preparation.

The reaction of the metal-organic precursor Fe[N(SiMe3)2]2 with H2 in the presence of a long-chain acid and a long-chain amine in various proportions produces monodisperse zerovalent iron nanoparticles. These Fe particles display magnetic properties that match those of bulk iron as evidenced by magnetic and Mössbauer measurements. The nanoparticles adopt a cubic shape with edges of 7 nanometers and are incorporated into extended crystalline superlattices containing nanocubes in close proximity and with their crystallographic axes aligned. These superlattices are formed in solution, precipitate in high yield, and may be redissolved and redeposited as two-dimensional arrays.

We measured the power spectrum and two-point correlation function for the randomly fluctuating free surface on the downstream side of a stationary flow with a maximum Froude number F_{max}≈0.85 reached above a localized obstacle. On such a flow the scattering of incident long wavelength modes is analogous to that responsible for black hole radiation (the Hawking effect). Our measurements of the noise show a clear correlation between pairs of modes of opposite energies. We also measure the scattering coefficients by applying the same analysis of correlations to waves produced by a wave maker.