arXiv subjects

Renaud Parentani

Publications and source records attributed to Renaud Parentani.

At least 55 records · Page 3Linked to original sources

arXiv2010

Black hole lasers in Bose-Einstein condensates

We consider elongated condensates that cross twice the speed of sound. In the absence of periodic boundary conditions, the phonon spectrum possesses a discrete and finite set of complex frequency modes that induce a laser effect. This effect constitutes a dynamical instability and is due to the fact that the supersonic region acts as a resonant cavity. We numerically compute the complex frequencies and density-density correlation function. We obtain patterns with very specific signatures. In terms of the gravitational analogy, the flows we consider correspond to a pair of black hole and white hole horizons, and the laser effect can be conceived as a self-amplified Hawking radiation. This is verified by comparing the outgoing flux at early time with the standard black hole radiation.

cond-mat.quant-gas↗

arXiv2010

Acoustic white holes in flowing atomic Bose-Einstein condensates

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.

cond-mat.quant-gas↗

arXiv2010

Black hole lasers, a mode analysis

We show that the black hole laser effect discovered by Corley & Jacobson should be described in terms of frequency eigenmodes that are spatially bound. The spectrum contains a discrete and finite set of complex frequency modes which appear in pairs and which encode the laser effect. In addition, it contains real frequency modes that form a continuous set when space is infinite, and which are only elastically scattered, i.e., not subject to any Bogoliubov transformation. The quantization is straightforward, but the calculation of the asymptotic fluxes is rather involved. When the number of complex frequency modes is small, our expressions differ from those given earlier. In particular, when the region between the horizons shrinks, there is a minimal distance under which no complex frequency mode exists, and no radiation is emitted. Finally, we relate this effect to other dynamical instabilities found for rotating black holes and in electric fields, and we give the conditions to get this type of instability.

hep-th↗

arXiv2010

From vacuum fluctuations across an event horizon to long distance correlations

We study the stress energy two-point function to show how short distance correlations across the horizon transform into correlations among asymptotic states, for the Unruh effect, and for black hole radiation. In the first case the transition is caused by the coupling to accelerated systems. In the second, the transition is more elusive and due to the change of the geometry from the near horizon region to the asymptotic one. The gradual transition is appropriately described by using affine coordinates. We relate this to the covariant regularization used to evaluate the mean value of the stress energy. We apply these considerations to analogue black holes, i.e. dispersive theories. On one hand, the preferred rest frame gives further insight about the transition, and on the other hand, the dispersion tames the singular behavior found on the horizon in relativistic theories.

gr-qc↗

arXiv2009

Black-hole radiation in Bose-Einstein condensates

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.

cond-mat.quant-gas↗

arXiv2009

Black/White hole radiation from dispersive theories

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 3x3 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. Application to four dimensional black holes and Bose-Einstein condensates are in preparation.

hep-th↗

arXiv2008

Inflationary Spectra from Lorentz Violating Dissipative Models

The sensitivity of inflationary spectra to initial conditions is addressed in the context of a phenomenological model that breaks Lorentz invariance by dissipative effects above some threshold energy $Λ$. These effects are obtained dynamically by coupling the fluctuation modes to extra degrees of freedom which are unobservable below $Λ$. Because of the strong dissipative effects in the early propagation, only the state of the extra degrees of freedom is relevant for the power spectrum. If this state is the ground state, and if $Λ$ is much larger than the Hubble scale $H$, the standard spectrum is recovered. Using analytical and numerical methods, we calculate the modifications for a large class of dissipative models. For all of these, we show that the leading modification (in an expansion in $H/Λ$) is linear in the decay rate evaluated at horizon exit, and that high frequency superimposed oscillations are not generated. The modification is negative when the decay rate decreases slower than the cube of $H$, which means that there is a loss of power on the largest scales.

hep-ph↗

arXiv2008

Signatures of trans-Planckian dispersion in inflationary spectra

The primordial spectra are calculated using dispersion relations which deviate from the relativistic one above a certain energy scale Lambda. We determine the properties of the leading modifications with respect to the standard spectra when Lambda is much greater than H, the Hubble scale during inflation. To be generic, we parameterize the lowest order deviation from the relativistic law by alpha, the power of P/Lambda where P is the proper momentum. When working in the asymptotic vacuum, the leading modification scales as (H/Lambda)^alpha for all alpha, except for a discrete set where the power is higher. Moreover, this modification is robust against introducing higher order terms in the dispersion relation. We then algebraically deduce the modifications of scalar and tensor power spectra in slow roll inflation from modifications calculated in de Sitter space. The modifications do not exhibit oscillations unless the dispersion relation induces some non-adiabaticity near a given scale. Finally, we explore the much less studied regime where H and Lambda are comparable. Our results indicate that the project of reconstructing the inflaton potential cannot be pursued without making some hypothesis about the dispersion relation of the fluctuation modes.

hep-th↗

arXiv2008

Horizon surface gravity as 2d geodesic expansion

The surface gravity of any Killing horizon, in any spacetime dimension, can be interpreted as a local, two-dimensional expansion rate seen by freely falling observers when they cross the horizon. Any two-dimensional congruence of geodesics invariant under the Killing flow can be used to define this expansion, provided that the observers have unit Killing energy.

gr-qc↗

arXiv2008

Confronting the trans-Planckian question of inflationary cosmology with dissipative effects

We provide a class of QFTs which exhibit dissipation above a threshold energy, thereby breaking Lorentz invariance. Unitarity is preserved by coupling the fields to additional degrees of freedom (heavy fields) which introduce the rest frame. Using the Equivalence Principle, we define these theories in arbitrary curved spacetime. We then confront the trans-Planckian question of inflationary cosmology. When dissipation increases with the energy, the quantum field describing adiabatic perturbations is completely damped at the onset of inflation. However it still exists as a composite operator made with the additional fields. And when these are in their ground state, the standard power spectrum obtains if the threshold energy is much larger that the Hubble parameter. In fact, as the energy redshifts below the threshold, the composite operator behaves as if it were a free field endowed with standard vacuum fluctuations. The relationship between our models and the Brane World scenarios studied by Libanov and Rubakov displaying similar effects is discussed. The signatures of dissipation will be studied in a forthcoming paper.

hep-th↗

arXiv2008

Decoherence and entropy of primordial fluctuations. I: Formalism and interpretation

We propose an operational definition of the entropy of cosmological perturbations based on a truncation of the hierarchy of Green functions. The value of the entropy is unambiguous despite gauge invariance and the renormalization procedure. At the first level of truncation, the reduced density matrices are Gaussian and the entropy is the only intrinsic quantity. In this case, the quantum-to-classical transition concerns the entanglement of modes of opposite wave-vectors, and the threshold of classicality is that of separability. The relations to other criteria of classicality are established. We explain why, during inflation, most of these criteria are not intrinsic. We complete our analysis by showing that all reduced density matrices can be written as statistical mixtures of minimal states, the squeezed properties of which are less constrained as the entropy increases. Pointer states therefore appear not to be relevant to the discussion. The entropy is calculated for various models in paper II.

hep-th↗

arXiv2008

Decoherence and entropy of primordial fluctuations II. The entropy budget

We calculate the entropy of adiabatic perturbations associated with a truncation of the hierarchy of Green functions at the first non trivial level, i.e. in a self-consistent Gaussian approximation. We give the equation governing the entropy growth and discuss its phenomenology. It is parameterized by two model-dependent kernels. We then examine two particular inflationary models, one with isocurvature perturbations, the other with corrections due to loops of matter fields. In the first model the entropy grows rapidely, while in the second the state remains pure (at one loop).

hep-th↗

arXiv2008

Constructing QFT's wherein Lorentz Invariance is broken by dissipative effects in the UV

There has been a recent interest in considering Quantum Field Theories in which Lorentz Invariance is broken in the UV sector. However attention has been mostly limited to dispersive theories. In this work we provide the generalized settings for studying dissipation. Unitarity is preserved by coupling the original fields to additional (heavy) fields which induce the dissipation. Starting with Lagrangians breaking LI in the UV, we learn that dissipative effects unavoidably develop in the effective theory. We then covariantize these Lagrangians in order to address the trans-Planckian question of inflation and black hole physics. The peculiar properties of the additional fields inducing dissipation is revealed by the covariantization. The links with the phenomenological approach to Quantum Gravity and with some Brane World scenarios are also discussed.

hep-th↗

arXiv2007

A Primer for Black Hole Quantum Physics

The mechanisms which give rise to Hawking radiation are revealed by analyzing in detail pair production in the presence of horizons. In preparation for the black hole problem, three preparatory problems are dwelt with at length: pair production in an external electric field, thermalization of a uniformly accelerated detector and accelerated mirrors. In the light of these examples, the black hole evaporation problem is then presented. The leitmotif is the singular behavior of modes on the horizon which gives rise to a steady rate of production. Special emphasis is put on how each produced particle contributes to the mean albeit arising from a particular vacuum fluctuation. It is the mean which drives the semiclassical back reaction. This aspect is analyzed in more detail than heretofore and in particular its drawbacks are emphasized. It is the semiclassical theory which gives rise to Hawking's famous equation for the loss of mass of the black hole due to evaporation $dM/dt \simeq -1/M^2$. Black hole thermodynamics is derived from the evaporation process whereupon the reservoir character of the black hole is manifest. The relation to the thermodynamics of the eternal black hole through the Hartle--Hawking vacuum and the Killing identity are displayed. It is through the analysis of the fluctuations of the field configurations which give rise to a particular Hawking photon that the dubious character of the semiclassical theory is manifest. The present frontier of research revolves around this problem and is principally concerned with the fact that one calls upon energy scales that are greater than Planckian and the possibility of a non unitary evolution as well. These last subjects are presented in qualitative fashion only, so that this review stops at the threshold of quantum gravity.

gr-qc↗

arXiv2007

Black hole entanglement entropy regularized in a freely falling frame

We compute the black hole horizon entanglement entropy S_E for a massless scalar field, first with a hard cutoff and then with high frequency dispersion, both imposed in a frame that falls freely across the horizon. Using WKB methods, we find that S_E is finite for a hard cutoff or super-luminal dispersion, because the mode oscillations do not diverge at the horizon and the contribution of high transverse momenta is cut off by the angular momentum barrier. For sub-luminal dispersion the entropy depends on the behavior at arbitrarily high transverse momenta. In all cases it scales with the horizon area. For the hard cutoff it is linear in the cutoff, rather than quadratic. This discrepancy from the familiar result arises from the difference between the free-fall frame and the static frame in which a cutoff is usually imposed. In the super-luminal case the entropy scales with a fractional power of the cutoff that depends on the index of the dispersion relation. Implications for the possible relation between regularized entanglement entropy and the Bekenstein-Hawking entropy are discussed.

hep-th↗

arXiv2007

Damped Corrections to Inflationary Spectra from a Fluctuating Cutoff

We reconsider trans-Planckian corrections to inflationary spectra by taking into account a physical effect which has been overlooked and which could have important consequences. We assume that the short length scale characterizing the new physics is endowed with a finite width, the origin of which could be found in quantum gravity. As a result, the leading corrections responsible for superimposed osillations in the CMB temperature anisotropies are generically damped by the blurring of the UV scale. To determine the observational ramifications of this damping, we compare it to that which effectively occurs when computing the angular power spectrum of temperature anisotropies. The former gives an overall change of the oscillation amplitudes whereas the latter depends on the angular scale. Therefore, in principle they could be distinguished. In any case, the observation of superimposed oscillations would place tight constraint on the variance of the UV cutoff.

hep-th↗

arXiv2007

Beyond the semi-classical description of black hole evaporation

In the semi-classical treatment, i.e. in a classical black hole geometry, Hawking quanta emerge from trans-Planckian configurations because of scale invariance. There is indeed no scale to stop the blue-shifting effect encountered in the backward propagation towards the event horizon. On the contrary, when taking into account the gravitational interactions neglected in the semi-classical treatment, a UV scale stopping the blue-shift could be dynamically engendered. To show that this is the case, we use a non-perturbative treatment based on the large-N limit, where $N$ is the number of matter fields. In this limit, the semi-classical treatment is the leading contribution. Non-linear gravitational effects appear in the next orders and in the first of these, the effects are governed by the two-point correlation function of the energy-momentum tensor evaluated in the vacuum. Taking this correlator into account, backward propagated modes are dissipated at a distance from the horizon $\propto Gκ$ when measured in a freely falling frame. ($G$ is Newton's constant and $κ$ the surface gravity.) This result can be also obtained by considering light propagation in a stochastic ensemble of metrics whose fluctuations are determined by the above correlator.

hep-th↗

arXiv2006

Inflationary spectra and violations of Bell inequalities

In spite of the macroscopic character of the primordial fluctuations, the standard inflationary distribution (that obtained using linear mode equations) exhibits inherently quantum properties, that is, properties which cannot be mimicked by any stochastic distribution. This is demonstrated by a Gedanken experiment for which certain Bell inequalities are violated. These violations are {\it in principle} measurable because, unlike for Hawking radiation from black holes, in inflationary cosmology we can have access to both members of correlated pairs of modes delivered in the same state. We then compute the effect of decoherence and show that the violations persist provided the decoherence level (and thus the entropy) lies below a certain non-vanishing threshold. Moreover, there exists a higher threshold above which no violation of any Bell inequality can occur. In this regime, the distributions are ``separable'' and can be interpreted as stochastic ensembles of fluctuations. Unfortunately, the precision which is required to have access to the quantum properties is so high that, {\it in practice}, an observational verification seems excluded.

astro-ph↗