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Mayoral, C., Recati, A., Fabbri, A., Parentani, R., Balbinot, R., & Carusotto, I. (2011). Acoustic white holes in flowing atomic Bose-Einstein condensates. New J. Phys., 13, 025007–29pp.
Abstract: We study acoustic white holes in a steadily flowing atomic Bose-Einstein condensate. A white hole configuration is obtained when the flow velocity goes from a super-sonic value in the upstream region to a sub-sonic one in the downstream region. The scattering of phonon wavepackets on a white hole horizon is numerically studied in terms of the Gross-Pitaevskii equation of mean-field theory: dynamical stability of the acoustic white hole is found, as well as a signature of a nonlinear back-action of the incident phonon wavepacket onto the horizon. The correlation pattern of density fluctuations is numerically studied by means of the truncated-Wigner method, which includes quantum fluctuations. Signatures of the white hole radiation of correlated phonon pairs by the horizon are characterized; analogies and differences with Hawking radiation from acoustic black holes are discussed. In particular, a short wavelength feature is identified in the density correlation function, whose amplitude steadily grows in time since the formation of the horizon. The numerical observations are quantitatively interpreted by means of an analytical Bogoliubov theory of quantum fluctuations for a white hole configuration within the step-like horizon approximation.
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Balbinot, R., & Fabbri, A. (2014). Amplifying the Hawking Signal in BECs. Adv. High. Energy Phys., 2014, 713574–8pp.
Abstract: We consider simple models of Bosep-Einstein condensates to study analog pairp-creation effects, namely, the Hawking effect from acoustic black holes and the dynamical Casimir effect in rapidly timep-dependent backgrounds. We also focus on a proposal by Cornell to amplify the Hawking signal in density-density correlators by reducing the atoms' interactions shortly before measurements are made.
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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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Dudley, R. A., Fabbri, A., Anderson, P. R., & Balbinot, R. (2020). Correlations between a Hawking particle and its partner in a 1+1D Bose-Einstein condensate analog black hole. Phys. Rev. D, 102(10), 105005–12pp.
Abstract: The Fourier transform of the density-density correlation function in a Bose-Einstein condensate (BEC) analog black hole is a useful tool to investigate correlations between the Hawking particles and their partners. It can be expressed in terms of <(out)(a) over cap (ext)(up) (out)(a) over cap (int)(up)> where (out)(a) over cap (ext)(up) is the annihilation operator for the Hawking particle and (out)(a) over cap (int)(up) is the corresponding one for the partner. This basic quantity is calculated for three different models for the BEC flow. It is shown that in each model the inclusion of the effective potential in the mode equations makes a significant difference. Furthermore, particle production induced by this effective potential in the interior of the black hole is studied for each model and shown to be nonthermal. An interesting peak that is related to the particle production and is present in some models is discussed.
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Carusotto, I., Balbinot, R., Fabbri, A., & Recati, A. (2010). Density correlations and analog dynamical Casimir emission of Bogoliubov phonons in modulated atomic Bose-Einstein condensates. Eur. Phys. J. D, 56(3), 391–404.
Abstract: We present a theory of the density correlations that appear in an atomic Bose-Einstein condensate as a consequence of the emission of correlated pairs of Bogoliubov phonons by a time-dependent atom-atom scattering length. This effect can be considered as a condensed matter analog of the dynamical Casimir effect of quantum field theory. Different regimes as a function of the temporal shape of the modulation are identified and a simple physical picture of the phenomenon is discussed. Analytical expressions for the density correlation function are provided for the most significant limiting cases. This theory is able to explain some unexpected features recently observed in numerical studies of analog Hawking radiation from acoustic black holes.
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Mauro, S., Balbinot, R., Fabbri, A., & Shapiro, I. L. (2015). Fourth derivative gravity in the auxiliary fields representation and application to the black-hole stability. Eur. Phys. J. Plus, 130(7), 135–8pp.
Abstract: We consider an auxiliary fields formulation for the general fourth-order gravity on an arbitrary curved background. The case of a Ricci-flat background is elaborated in detail and it is shown that there is an equivalence with the standard metric formulation. At the same time, using auxiliary fields helps to make perturbations to look simpler and the results clearer. As an application we reconsider the linear perturbations for the classical Schwarzschild solution. We also briefly discuss the relation to the effect of massive unphysical ghosts in the theory.
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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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Balbinot, R., Fabbri, A., & Mayoral, C. (2013). Hawking effect in BECs acoustic white holes. Eur. Phys. J. Plus, 128(2), 16–21pp.
Abstract: Bogoliubov pseudoparticle creation in a BEC undergoing a WH-like flow is investigated analytically in the case of a one-dimensional geometry with stepwise homogeneous regions. Comparison of the results with those corresponding to a BH flow is performed. The implications for the analogous gravitational problem is 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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Coutant, A., Fabbri, A., Parentani, R., Balbinot, R., & Anderson, P. R. (2012). Hawking radiation of massive modes and undulations. Phys. Rev. D, 86(6), 064022–17pp.
Abstract: We compute the analogue Hawking radiation for modes which possess a small wave vector perpendicular to the horizon. For low frequencies, the resulting mass term induces a total reflection. This reflection is accompanied by an extra mode mixing which occurs in the supersonic region, and which cancels out the infrared divergence of the near horizon spectrum. As a result, the amplitude of the undulation (0-frequency wave with macroscopic amplitude) emitted in white hole flows now saturates at the linear level, unlike what is found in the massless case. In addition, we point out that the mass introduces a new type of undulation which is produced in black hole flows, and which is well described in the hydrodynamical regime.
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