Outgoing Modes Research Articles

The Hawking temperature of dynamical black holes via conformal transformations

In this second part of our two-series on extracting the Hawking temperature of dynamical black holes, we focus into spacetimes that are conformal transformations of static spacetimes. Our previous investigation builds upon the Unruh–Hawking analogy, which relates the spacetime of a uniformly accelerating observer to the near-horizon region of a black hole, to obtain the Hawking temperature. However, in this work, we explicitly compute the Bogoliubov coefficients associated with incoming and outgoing modes, which not only yields the temperature but also thermal spectrum of particles emitted by a black hole. For illustration, we take the simplest nontrivial example of the linear Vaidya spacetime, which is conformal to the static metric and using this property, we analytically solve the massless scalar field in its background. This allows the explicit computations of the Bogoliubov coefficients to study the particle production in this spacetime. We also derive an expression for the total mass of such dynamical spacetimes using the conformal Killing vector. We then perform differential variations of the mass formula to determine whether the laws of dynamical black hole mechanics correspond to the laws of thermodynamics.

Subwavelength resonant acoustic scattering in fast time-modulated media

This article provides a rigorous mathematical analysis of acoustic wave scattering induced by a high-contrast subwavelength resonator whose material density is periodically modulated in time, and with a modulation frequency that is much larger than the one of the incident wave. We find that in general, the effect of the fast modulation is averaged over time and that the system behaves as an unmodulated resonator with an apparent effective density. However, under a suitable tuning of the modulation, which achieves a matching between temporal Sturm-Liouville and spatial Neumann eigenvalues, the low frequency incident wave becomes suddenly able to excite high frequency modes in the resonator. This phenomenon leads to the generation of scattered waves carrying high frequency components in the far field, and to the existence of exponentially growing outgoing modes. From these findings, it is expected that such time-modulated system could serve as a spontaneously radiating device, or as a high harmonic generator.

Achieving the Fundamental Quantum Limit of Linear Waveform Estimation.

Sensing a classical signal using a linear quantum device is a pervasive application of quantum-enhanced measurement. The fundamental precision limits of linear waveform estimation, however, are not fully understood. In certain cases, there is an unexplained gap between the known waveform-estimation quantum Cramér-Rao bound and the optimal sensitivity from quadrature measurement of the outgoing mode from the device. We resolve this gap by establishing the fundamental precision limit, the waveform-estimation Holevo Cramér-Rao bound, and how to achieve it using a nonstationary measurement. We apply our results to detuned gravitational-wave interferometry to accelerate the search for postmerger remnants from binary neutron-star mergers. If we have an unequal weighting between estimating the signal's power and phase, then we propose how to further improve the signal-to-noise ratio by a factor of sqrt[2] using this nonstationary measurement.

Lead Green's functions from quadratic eigenvalue problems without mode velocity calculations.

In quantum transport calculations, the proper handling of incoming and outgoing modes for retarded Green's functions is achieved via the lead self-energies. Computationally efficient and accurate methods to calculate the self-energies are thus very important. Here we present an alternative method for calculating lead self-energies which improves on a standard approach to solving quadratic eigenvalue problems that arise in quantum transport modeling. The method is based on a perturbative analysis of the generalized Schur decomposition to determine the relevant set of eigenvalues for transmitting modes. This allows us to circumvent finding the velocities of the modes (left- or right-moving) that are needed in order to calculate the lead Green's function from translationally invariant Green's functions. This saves computational time irrespective of the value of the imaginary part added to the energy. We compare our method with two existing methods-a popular iterative method and a standard eigenvalue method that explicitly calculates the velocities of the propagating modes. Our comparison shows that both eigenvalue methods are more robust than the iterative method. Furthermore, the comparison also shows that above a small threshold of propagating modes, the standard eigenvalue method requires extra computation time over our perturbation method. This excess of computation time grows linearly with the number of propagating modes.

Callan-Rubakov effect and higher charge monopoles

In this paper we study the interaction between magnetic monopoles and massless fermions. In the low energy limit, the monopole’s magnetic field polarizes the fermions into purely in-going and out-going modes. Consistency requires that the UV fermion-monopole interaction leads to non-trivial IR boundary conditions that relate the in-going to out-going modes. These non-trivial boundary conditions lead to what is known as the Callan-Rubakov effect. Here we derive the effective boundary condition by explicitly integrating out the UV degrees of freedom for the general class of spherically symmetric SU(N) monopoles coupled to massless fermions of arbitrary representation. We then show that the boundary conditions preserve symmetries without ABJ-type anomalies. As an application we explicitly derive the boundary conditions for the stable, spherically symmetric monopoles associated to the SU(5) Georgi-Glashow model and comment on the relation to baryon number violation.

Proposal of a module-driven architecture for building simulation models devoted to container terminals: dilemmas in applying generic, flexible, and modular principles

Container terminals are complex systems where containerized cargo undergoes a set of processing and handling operations to be delivered to their outgoing modes. A pool of decision support methods and simulation models has been developed to assist planners and managers in making decisions about daily operations. Nevertheless, most are designed for a particular terminal and not generic types. Indeed, a generic model serves as a conceptual factory to create specific models which greatly reduces the time and efforts of development; however, building such a model is no mean feat. To this aim, the paper on hand discusses the complexity of applying genericity, flexibility, and modularity in system modeling and proposes a generic architecture to build modular and flexible simulation models for container terminals. This architecture is split into a set of smaller, manageable, well-connected, and generic modules that facilitate the creation of highly parametrized specific models. An illustrative example of the architecture usage is presented in a case study, the new container terminal of Stockholm, and the resulting models were validated by subject matter experts. Finally, to prove its efficiency, a numerical study fed with real data is conducted to investigate the handling capacity of the studied system under different handling and flow scenarios. The obtained results show that the terminal handling capacity can be increased by around 50% if three to four more straddle carriers are added to the existing fleet.

Development of the new employment forms in the context of digital transformation of the economy

The article deals with the problems of the formation of new forms of employment under the influence of digitalisation processes and a protracted economic crisis. The purpose of the study is to consider the little-studied aspects of development of the new forms of employment in the conditions of the “fourth industrial revolution” and determine their prospects. The work shows that the spread of new forms of employment in the context of the formation of a new technological order indicates the digital transformation of the economy and at the same time acts as a response to the economic crisis caused by the obsolescence of the industries of the outgoing modes due to the gradual exhaustion of their efficiency, including impact of the recent COVID-19 pandemic. At the same time, the introduction of new elements of employment into the system of social and labor relations does not eliminate the previously existing conflicts of interests of their participants, but ensures a more dynamic development of the labor market and increases the adaptive potential of workers. Particular attention is paid to such forms of work organization as mobile work based on information and communication technologies, work on platforms and sharing of employees’ labor. The authors conduct a comparative analysis of the advantages and disadvantages of these forms of employment based on employers’ and employees’ interests and points of view. Reserves of growth and restrictions on the development of new forms of employment have been identified. Attention is focused on the social and cultural consequences of increased flexibility and mobility of labor relations in the context of the development of new non-standard forms of employment. The results of the study can be used in developing areas for improvement of employment policy in the context of further deployment of digitalisation processes.

Finding pythons in unexpected places

We argue that novel (highly nonclassical) quantum extremal surfaces (QESs) play a crucial role in reconstructing the black hole interior even for isolated, single-sided, non-evaporating black holes (i.e. with no auxiliary reservoir). Specifically, any code subspace where interior outgoing modes can be excited will have a QES in its maximally mixed state. We argue that as a result, reconstruction of interior outgoing modes is always exponentially complex. Our construction provides evidence in favor of a strong python’s lunch proposal: that nonminimal QESs are the exclusive source of exponential complexity in the holographic dictionary. We also comment on the relevance of these QESs to the geometrization of state dependence in the typicality arguments for firewalls.

Interferometry of black holes with Hawking radiation

We investigate the wave optical imaging of black holes with Hawking radiation. The spatial correlation function of Hawking radiation is expressed in terms of transmission and reflection coefficients for scalar wave modes and evaluated by numerically summing over angular quantum numbers for the Unruh-Hawking state of the Kerr-de Sitter black hole. Then, wave optical images of an evaporating black hole are obtained by the Fourier transformation of the spatial correlation function. For short wavelength, the image of the black hole with the outgoing mode of the Unruh-Hawking state has the appearance of a star with its surface given by the photon sphere. It is found that interference between incoming modes from the cosmological horizon and reflected modes due to the scattering of the black hole can enhance brightness of images in the vicinity of the photon sphere. For a long wavelength, the entire field of view is bright, and the emission region of Hawking radiation cannot be identified.

Real-time motion of open quantum systems: Structure of entanglement, renormalization group, and trajectories

In this paper, we provide a complete description of the life cycle of entanglement during the real-time motion of open quantum systems. The quantum environment can have arbitrary (e.g., structured) spectral density. The entanglement can be seen constructively as a Lego: its bricks are the modes of the environment. These bricks are connected to each other via operator transforms. The central result is that during each infinitesimal time interval one new (incoming) mode of the environment gets coupled (entangled) to the open system, and one new (outgoing) mode gets irreversibly decoupled (disentangled from the future). Moreover, each moment of time, only a few relevant modes (three to four in the considered cases) are non-negligibly coupled to the future quantum motion. These relevant modes change (flow or renormalize) with time. As a result, the temporal entanglement has the structure of a matrix-product operator. This allows us to pose a number of questions and to answer them in this paper: What is the intrinsic quantum complexity of a real time motion? Does this complexity saturate with time or grow without bounds? How does one do the real-time renormalization group in a justified way? How do the classical Brownian stochastic trajectories emerge from the quantum evolution? How does one construct the few-mode representations of non-Markovian environments? We provide illustrative simulations of the spin-boson model for various spectral densities of the environment: semicircle, subohmic, ohmic, and superohmic.

Infrared signatures of a quantum bounce in a minisuperspace analysis of Lemaître-Tolman-Bondi dust collapse

In the quantum treatment of collapsing matter, a viable mode analysis is supposed to give information regarding emission during the collapse. Nevertheless, partly owing to operator ordering ambiguities involved in a typical quantum gravity analysis, the availability of such well-defined modes is not guaranteed. We study the mode decomposition of the unitarily evolving wave packet constructed for the quantum model of spherically symmetric dust collapsing in a marginally bound Lema\^{\i}tre-Tolman-Bondi (LTB) model. We identify the observable depicting mode decomposition, and using the freedom of operator ordering ambiguity, we obtain the Hermitian extension of this operator alongside the Hermitian Hamiltonian. After identifying incoming and outgoing modes with this operator's eigenstates, we estimate their contributions to the radiation profile. The infrared sector of this process demonstrates some characteristic features which turn out to be highly sensitive to the near-bounce dynamics of the dust cloud. Near the epoch of classical singularity, there is a significant contribution from incoming/outgoing modes of small wavenumber in the expanding/collapsing phase of the dust cloud, which keeps on decreasing as one moves away from the singularity. The information of the bounce is carried over to the infrared modes through a flip from largely incoming to largely outgoing radiation as the evolution progresses from collapsing to expanding phase, much before the information of bounce comes about to any observer. In the infrared sector, the saturation value of the amplitude marks the bounce radius. Thus, we argue that the information of the short scale physics is essentially carried over to the longest wavelength in this quantum gravity model, which we argue is rather more prominent for low energy processes.

Instability of de Sitter space under thermal radiation in different vacua

We study the instability of de Sitter space-time (dS) under thermal radiation in different vacua.We argue that the mode function solution of a scalar field in four-dimensional dS can be separated into the incoming and outgoing modes. Different vacua for dS are realized by different combinations of positive frequency modes assigned to each solution. For a minimally coupled massless scalar field, we explicitly compute the behavior of the mode function and the corresponding energy-momentum tensor in the Unruh vacuum near the horizon, and find that the horizon area increases (decreases) in time when the incoming (outgoing) mode contributes to thermal flux.

Driving plasmonic nanoantennas at perfect impedance matching using generalized coherent perfect absorption

Abstract Coherent perfect absorption (CPA) describes the absence of all outgoing modes from a lossy resonator, driven by lossless incoming modes. Here, we show that for nanoresonators that also exhibit radiative losses, e.g., plasmonic nanoantennas, a generalized version of CPA (gCPA) can be applied. In gCPA outgoing modes are suppressed only for a subset of (guided plasmonic) modes while other (radiative) modes are treated as additional loss channels - a situation typically referred to as perfect impedance matching. Here we make use of gCPA to show how to achieve perfect impedance matching between a single nanowire plasmonic waveguide and a plasmonic nanoantenna. Antennas with both radiant and subradiant characteristics are considered. We further demonstrate potential applications in background-free sensing.

Observer-dependent black hole interior from operator collision

We present concrete construction of interior operators for a black hole which is perturbed by an infalling observer. The construction is independent from the initial states of the black hole while dependent only on the quantum state of the infalling observer. The construction has a natural interpretation from the perspective of the boundary operator's growth, resulting from the collision between operators accounting for the infalling and outgoing modes. The interior partner modes are created once the infalling observer measures the outgoing mode, suggesting that the black hole interior is observer dependent. Implications of our results on various conceptual puzzles, including the firewall puzzle, the Marolf-Wall puzzle, and the information problem, are discussed. Explicit counterarguments against the $\mathrm{ER}=\mathrm{EPR}$ approach by Maldacena and Susskind are also presented.

Heating up an environment around black holes and inside de Sitter space

We study quantum fields on spacetimes having a bifurcate Killing horizon by allowing the possibility that left- and right- (in-going and out-going) modes have different temperatures. We consider in particular the Rindler for both massless and massive fields, the static de Sitter and Schwarzschild black hole backgrounds for massive fields. We find that in all three cases, when any of the temperatures is different from the canonical one (Unruh, Hawking and Gibbons--Hawking, correspondingly) the correlation functions have extra singularities at the horizon.

Observables in quantum field theory on a collapsing black hole background

We study the quantum radiation from a curved background using scalar observables constructed from the (1+1) dimensional renormalized stress-energy tensor (RSET). We compute energy density U, flux F and pressure P for an arbitrary collapse scenario and an arbitrary observer. The results show a clear structure: F−U represents the collapse-independent ingoing modes, F+U represents the collapse-dependent outgoing modes and P−U represents the trace anomaly. We also compute the observables constructed from the perception renormalized stress-energy tensor (PeRSET). We find they have the same collapse-dependent contribution comparing to their RSET-related counterparts. For free-falling observers, in particular, the PeRSET-related observables are the same as the corresponding RSET-related ones, except the energy densities differ by the trace anomaly.

Information loss paradox revisited: Farewell firewall?

Unitary evolution makes pure state on one Cauchy surface evolve to pure state on another Cauchy surface. Outgoing Hawking radiation is the only subsystem on the late Cauchy surface. The requirement that Hawking radiation should be pure amounts to requiring purity of the subsystem when the total system is pure. We will see that this requirement will lead to firewall even in flat spacetime, and thus is invalid. Information is either stored in the entanglement between field modes inside black hole and the outgoing modes or stored in correlation between geometry and Hawking radiation when singularity is resolved by quantum gravity effects. We will give a simple argument that even in semi-classical regime, information is (at least partly) stored in correlation between geometry and Hawking radiation.

Holographic chaos, pole-skipping, and regularity

Abstract We investigate the “pole-skipping” phenomenon in holographic chaos. According to pole-skipping, the energy-density Green’s function is not unique at a special point in the complex momentum plane. This arises because the bulk field equation has two regular near-horizon solutions at the special point. We study the regularity of the two solutions more carefully using curvature invariants. In the upper-half $\omega$-plane, one solution, which is normally interpreted as the outgoing mode, is in general singular at the future horizon and produces a curvature singularity. However, at the special point, both solutions are indeed regular. Moreover, the incoming mode cannot be uniquely defined at the special point due to these solutions.

OAM Mode Order Conversion and Clutter Rejection With OAM-Coded RFID Tags

In this article, a uniform helically arranged dielectric resonator array can generate Orbital Angular Momentum waves (OAM) causing a conversion of OAM mode orders $m$ from an incoming mode ${m}_{in}$ to an outgoing mode ${m}_{out}$ . The operating frequency is set as 10 GHz to facilitate the measuring process. This new approach provides additional OAM values per digit in the RFID technology according to the excited OAM modes ${m}_{n}\,\,\in \,\,\{\ldots,-2,-1,0,1,2,\ldots \}$ instead of the conventional binary values ${b}_{n}~\in ~\{0, 1\}$ . Thus, more information content is revealed. Through the OAM concept, a ${m}_{1} {m}_{2}~2$ -digits OAM coded tag is obtained upon the employment of two uniform helically arranged cylindrical dielectric resonator arrays operating at two different frequencies ${f}_{1} = 10\,\,\text {GHz}$ , and ${f}_{2} = 11\,\,\text {GHz}$ . Each array has 8 DRs but with different radius yielding a reduction of the mutual coupling between the varied circular arrays. The interaction between the phase delayed radiation of each DR element in the array generates different vortex waves with corresponding OAM mode orders. In order to achieve the correct phase delay, the elevation of each DR is specified by the desirable OAM mode order, the number of elements and the propagation wavelength. At first, the generation of OAM mode orders −1, 2, and −3 is carried out. Then, mode conversion from 0 to −1, +1 to −2, −1 to 0, +2 to −3, and −2 to +1 are depicted. After that, two simulated examples of 2-digits OAM coded tags with the code $\{-1,1\}$ and $\{-2,0\}$ are presented. A conversion of mode 0 to mode 1 has been simulated and also measured, where an additional metal sheet is used to evaluate the distortion in the OAM modes. As a result, this study demonstrates that the uniform helically arranged DR arrays can convert the incoming OAM mode order into another one, where the clutter from broadside direction is rejected due to the Butler matrix (BM), which interferes the clutter destructively.

Soft mode and interior operator in the Hayden-Preskill thought experiment

We study the smoothness of the black hole horizon in the Hayden-Preskill thought experiment by using two particular toy models based on variants of Haar random unitary. The first toy model corresponds to the case where the coarse-grained entropy of a black hole is larger than its entanglement entropy. We find that, while the outgoing mode and the remaining black hole are entangled, the Hayden-Preskill recovery cannot be performed. The second toy model corresponds to the case where the system consists of low energy soft modes and high energy heavy modes. We find that the Hayden-Preskill recovery protocol can be carried out via soft modes whereas heavy modes give rise to classical correlations between the outgoing mode and the remaining black hole. We also point out that the procedure of constructing the interior partners of the outgoing soft mode operators can be interpreted as the Hayden-Preskill recovery, and as such, the known recovery protocol enables us to explicitly write down the interior operators. Hence, while the infalling mode needs to be described jointly by the remaining black hole and the early radiation in our toy model, adding a few extra qubits from the early radiation is sufficient to reconstruct the interior operators.