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Fabbri, A., Balbinot, R., & Anderson, P. R. (2016). Scattering coefficients and gray-body factor for 1D BEC acoustic black holes: Exact results. Phys. Rev. D, 93(6), 064046–6pp.
Abstract: A complete set of exact analytic solutions to the mode equation is found in the region exterior to the acoustic horizon for a class of 1D Bose-Einstein condensate acoustic black holes. From these, analytic expressions for the scattering coefficients and gray-body factor are obtained. The results are used to verify previous predictions regarding the behaviors of the scattering coefficients and gray-body factor in the low-frequency limit.
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Dudley, R. A., Anderson, P. R., Balbinot, R., & Fabbri, A. (2018). Correlation patterns from massive phonons in 1+1 dimensional acoustic black holes: A toy model. Phys. Rev. D, 98(12), 124011–18pp.
Abstract: Transverse excitations in analogue black holes induce a masslike term in the longitudinal mode equation. With a simple toy model we show that correlation functions display a rather rich structure characterized by groups of approximately parallel peaks. For the most part the structure is completely different from that found in the massless case.
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Anderson, P. R., Fabbri, A., & Balbinot, R. (2015). Low frequency gray-body factors and infrared divergences: Rigorous results. Phys. Rev. D, 91(6), 064061–18pp.
Abstract: Formal solutions to the mode equations for both spherically symmetric black holes and Bose-Einstein condensate acoustic black holes are obtained by writing the spatial part of the mode equation as a linear Volterra integral equation of the second kind. The solutions work for a massless minimally coupled scalar field in the s-wave or zero angular momentum sector for a spherically symmetric black hole and in the longitudinal sector of a one-dimensional Bose-Einstein condensate acoustic black hole. These solutions are used to obtain in a rigorous way analytic expressions for the scattering coefficients and gray-body factors in the zero frequency limit. They are also used to study the infrared behaviors of the symmetric two-point function and two functions derived from it: the point-split stress-energy tensor for the massless minimally coupled scalar field in Schwarzschild-de Sitter spacetime and the density-density correlation function for a Bose-Einstein condensate acoustic black hole.
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Anderson, P. R., Balbinot, R., Fabbri, A., & Parentani, R. (2014). Gray-body factor and infrared divergences in 1D BEC acoustic black holes. Phys. Rev. D, 90(10), 104044–6pp.
Abstract: It is shown that the gray-body factor for a one-dimensional elongated Bose-Einstein condensate (BEC) acoustic black hole with one horizon does not vanish in the low-frequency (omega -> 0) limit. This implies that the analog Hawking radiation is dominated by the emission of an infinite number (1/omega) of soft phonons in contrast with the case of a Schwarzschild black hole where the gray-body factor vanishes as omega -> 0 and the spectrum is not dominated by low-energy particles. The infrared behaviors of certain correlation functions are also discussed.
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Anderson, P. R., Balbinot, R., Fabbri, A., & Parentani, R. (2013). Hawking radiation correlations in Bose-Einstein condensates using quantum field theory in curved space. Phys. Rev. D, 87(12), 124018–18pp.
Abstract: The density-density correlation function is computed for the Bogoliubov pseudoparticles created in a Bose-Einstein condensate undergoing a black hole flow. On the basis of the gravitational analogy, the method used relies only on quantum field theory in curved spacetime techniques. A comparison with the results obtained by ab initio full condensed matter calculations is given, confirming the validity of the approximation used, provided the profile of the flow varies smoothly on scales compared to the condensate healing length.
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