Flat Power Spectrum Research Articles

A 25-micrometer Single-Photon-Sensitive Kinetic Inductance Detector

We report measurements characterizing the performance of a kinetic inductance detector array designed for a wavelength of 25 microns and very low optical background level suitable for applications such as a far-infrared instrument on a cryogenically cooled space telescope. In a pulse-counting mode of operation at low optical flux, the detectors can resolve individual 25-micron photons. In an integrating mode, the detectors remain photon noise limited over more than 6 orders of magnitude in absorbed power from 70 zW to 200 fW, with a limiting noise equivalent power of 4.6×10−20 W Hz−1 at 1 Hz. In addition, the detectors are highly stable with flat power spectra under optical load down to 1 mHz. Operational parameters of the detector are determined including the efficiency of conversion of the incident optical power into quasiparticles in the aluminum absorbing element and the quasiparticle self-recombination constant. Published by the American Physical Society 2024

Large extra dimensions from higher-dimensional inflation

We propose the possibility that compact extra dimensions can obtain large size by higher-dimensional inflation, relating the weakness of the actual gravitational force to the size of the observable Universe. Solution to the horizon problem implies that the fundamental scale of gravity is smaller than 1013 GeV, which can be realized in a braneworld framework for any number of extra dimensions. However, requirement of an (approximate) flat power spectrum of primordial density fluctuations consistent with present observations makes this simple proposal possible only for one extra dimension at around the micron scale. After the end of five-dimensional inflation, the radion modulus can be stabilized at a vacuum with positive energy of the order of the present dark energy scale. An attractive possibility is based on the contribution to the Casimir energy of right-handed neutrinos with a mass at a similar scale. Published by the American Physical Society 2024

Fraudulent white noise: Flat power spectra belie arbitrarily complex processes

Power spectral densities are a common, convenient, and powerful way to analyze signals, so much so that they are now broadly deployed across the sciences and engineering—from quantum physics to cosmology and from crystallography to neuroscience to speech recognition. The features they reveal not only identify prominent signal frequencies but also hint at mechanisms that generate correlation and lead to resonance. Despite their near-centuries-long run of successes in signal analysis, here we show that flat power spectra can be generated by highly complex processes, effectively hiding all inherent structure in complex signals. Historically, this circumstance has been widely misinterpreted, being taken as the renowned signature of “structureless” white noise—the benchmark of randomness. We argue, in contrast, to the extent that most real-world complex systems exhibit correlations beyond pairwise statistics their structures evade power spectra and other pairwise statistical measures. As concrete physical examples, we demonstrate that fraudulent white noise hides the predictable structure of both entangled quantum systems and chaotic crystals. To make these words of warning operational, we present constructive results that explore how this situation comes about and the high toll it takes in understanding complex mechanisms. First, we give the closed-form solution for the power spectrum of a very broad class of structurally complex signal generators. Second, we demonstrate the close relationship between eigenspectra of evolution operators and power spectra. Third, we characterize the minimal generative structure implied by any power spectrum. Fourth, we show how to construct arbitrarily complex processes with flat power spectra. Finally, leveraging this diagnosis of the problem, we point the way to developing more incisive tools for discovering structure in complex signals.10 MoreReceived 6 July 2020Accepted 16 December 2020DOI:https://doi.org/10.1103/PhysRevResearch.3.013170Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasChaosComplex systemsFluctuations & noiseInformation & communication theoryNoiseStochastic processesNonlinear DynamicsInterdisciplinary PhysicsStatistical PhysicsGeneral Physics

GNSS C/N0 degradation model in presence of continuous wave and pulsed interference

<h3>Abstract</h3> In the Global Navigation Satellite System (GNSS) L5/E5a interference environment, RTCA DO-292 proposes a model to compute the <i>C/N</i>₀ degradation due to the presence of interference signals, such as Distance Measuring Equipment/TACtical Air Navigation (DME/TACAN), Joint Tactical Information Distribution System/Multifunctional Information Distribution System (JTIDS/MIDS), etc., and due to the application of a temporal blanker to mitigate their impact. The <i>C/N</i>₀ degradation is modeled as a function of the blanker duty cycle, <i>bdc</i>, and the equivalent noise-level contribution of the non-blanked interference, <i>R_I</i>. However, in RTCA DO-292, the computation of these two terms has a reduced accuracy since a general statistical model of signal pulse collisions and an overbounded flat post-blanker pulsed interference signal Power Spectrum Density (PSD) are assumed. In this paper, the limitations of the applied pulse collisions mathematical model are commented, and the use of true post-blanker pulsed interference signal PSD is introduced through the application of the spectral separation coefficient. As a result, more accurate new formulas for <i>R_I</i> and <i>C/N</i>₀ degradation are derived. The new formulas are verified through simulations for DME/TACAN signals.

Abundance of primordial black holes in peak theory for an arbitrary power spectrum

Abstract We modify the procedure for estimating the primordial black hole (PBH) abundance proposed in [C.-M. Yoo, T. Harada, J. Garriga, and K. Kohri, Prog. Theor. Exp. Phys. 2018, 123E01 (2018)] so that it can be applied to a broad power spectrum such as the scale-invariant flat power spectrum. In the new procedure we focus on peaks of the Laplacian of the curvature perturbation $\Delta \zeta$, and use the values of $\Delta \zeta$ and $\Delta \Delta \zeta $ at each peak to specify the profile of $\zeta$ as a function of the radial coordinate; the values of $\zeta$ and $\Delta \zeta$ are used in the previous paper. The new procedure decouples the larger-scale environmental effect from the estimate of PBH abundance. Because the redundant variance due to the environmental effect is eliminated, we obtain a narrower shape of the mass spectrum compared to the previous procedure. Furthermore, the new procedure allows us to estimate the PBH abundance for the scale-invariant flat power spectrum by introducing a window function. Although the final result depends on the choice of the window function, we show that the $k$-space tophat window minimizes the extra reduction of the mass spectrum due to the window function. That is, the $k$-space tophat window has the minimum required property in the theoretical PBH estimation. Our procedure makes it possible to calculate the PBH mass spectrum for an arbitrary power spectrum by using a plausible PBH formation criterion with the nonlinear relation taken into account.

Optical Amplifier Response Estimation Considering Non-Flat Input Signals Characterization Based on Artificial Neural Networks

Optical communication systems are facing the challenge to become robust to dynamic operating conditions, thus requiring autonomous devices. Optical amplifiers are essential devices for establishing optical communication systems with good quality of transmission. However, optical amplifiers include noise and present a non-flat spectral response. As a consequence, simple regression methods are not suitable for modeling amplifier response. The amplifier output signal estimation has been studied in other works. However, all the previous works only use characterization data with a flat input signal power spectrum, which can decrease the accuracy of the previous estimators when the amplifiers are under real-world conditions. In this work, we proposed models based on an artificial neural network to estimate the optical amplifier output signal considering characterization data with non-flat signals. The results show that the previous models, proposed for flat characterization, do not perform well with non-flat data. The results obtained by the new models are promising since they returned a smaller estimation error than the previous models. We observed an error reduction of 4 dB when compared with the previous models under certain circumstances. Moreover, the proposed models are robust even when we use limited non-flat data in the training process.

Generation of laser chaos with wide-band flat power spectrum in a circular-side hexagonal resonator microlaser with optical feedback.

We numerically demonstrate the generation of wide-band laser chaos with flat power spectrum in a 2D circular-side hexagonal resonator (CSHR) microlaser subject to long-cavity optical feedback. The bandwidth and flatness of the chaotic power spectrum are investigated under different bias currents and optical feedback rates. Under low bias current, the bandwidth under an optimized optical feedback rate increases obviously as raising bias current and the power spectrum flatten simultaneously. Under high bias current, the optimized bandwidth gradually tends toward stabilization, with corresponding flatness less than 5 dB. We compare the chaotic power spectra with small-signal modulation response (SSR) curves under different bias currents. It can be concluded that wide-band and flat SSR indicates wide-band and flat chaotic power spectrum. This work argues that we can enhance laser chaos by using a laser device with wide-band and flat SSR and simple optical feedback configuration, which is significantly beneficial to synchronization-based applications including chaos communication and key distribution.

A Method to Determine the Electret Charge Potential of MEMS Vibrational Energy Harvester Using Pure-White Noise

A high-speed measurement method has been developed to electrically determine the potential voltage of the permanent charge or electret formed in a MEMS (microelectromechanical systems) vibrational energy harvester. While the conventional admittance method requires long time to observe the waveforms of the output power in time domain that diminishes when the built-in electret potential is compensated by an external voltage, this work proposes a new method to uniquely and promptly determine the electret potential by using the FFT (fast Fourier transform) analysis on the vibrational energy harvester excited by the white-noise voltage; the resonant peak in the frequency domain diminishes when the electret potential is compensated by the applied external bias voltage. White noise has been used in conventional method to measure the frequency response of devices of linear characteristics. However, due to the randomness of the input signal, random noise is inherently introduced to the measurement result, which urges us to repeat the measurement and to perform time-averaging to smooth out the noise. Therefore we used a newly developed white noise so-called “pure” white noise, which has a totally flat power spectrum, as it is synthesized from waveforms of a constant magnitude and random phases. We compute the inverse Fourier transform of such pure-white noises to instantly obtain the power spectrum without using mathematical averaging, and thus the throughput of measurement is enhanced ten-times faster.

A Hybrid Chaotic Encryption Scheme for Wireless Body Area Networks

Wireless body area network is a low-power and high-security wireless communication protocol specially used in the medical environment. It requires a highly secure encryption algorithm to ensure that information related to a patient’s vital signs cannot be accessed by an attacker. In this article, a security scheme based on chaotic mapping for WBAN is proposed. This algorithm makes use of the hybrid chaotic system obtained by the combination of Logistic and Tent mapping as the sequence generator, which can select the effective precision according to the importance of the transmitted information to ensure the reasonable allocation of computing resources, including floating-point encryption, fixed-point 32-bit encryption, fixed-point 24-bit encryption, and fixed-point 16-bit encryption. In the randomness test of the sequence, it can be seen that the sequence autocorrelation coefficient generated by the combined chaotic system is close to 0 and has a flat power spectrum. At the same time, the sequences produced by the floating-point system and 32-bit fixed-point system have passed the NIST test, which proves that combined chaos overcomes the influence of sequence length and finite precision. Experimental analysis and performance comparison show that the proposed encryption algorithm has sufficient security to resist common attacks.

Multivariable extremum-seeking by periodic switching functions with application to Raman optical amplifiers

A periodic switching function based extremum-seeking sliding-mode control strategy is addressed for uncertain nonlinear systems. We generalize previous results to a more challenging multivariable scenario, where the diagonal dominance condition is relaxed and can now be understood as a triangular dominance condition, which is significantly less restrictive. As an essential advantage over earlier results in the literature, the complete global convergence proof (with respect to the closed-loop initial conditions) of the overall multi-input multi-output (MIMO) closed-loop system is provided, rather than local stability results. The practical application of the proposed multivariable controller is exemplified through the optimization problem of the output signal power spectrum of Raman optical amplifiers. From a practical point of view, the extremum-seeking scheme enables the automatic adjustment of the control pump power signals in the presence of plant uncertainties, guaranteeing a flat power spectrum of the downstream data signals. Using a multi-objective approach, we develop the optimization algorithm to achieve this goal by simultaneously minimizing the output ripple and the deviation from some desired power level. The convergence analysis and control design are carried out in the presence of uncertainties, and the algorithm performance is tested through numerical examples, where a particular optical communication system with 32 channels is considered. This numerical example uses model parameters acquired experimentally and a representative fiber model, such that the results are close to what is expected to find in a practical implementation.

Spatial power spectra of dust across the Local Group: No constraint on disc scale height

ABSTRACT We analyse the 1D spatial power spectra of dust surface density and mid to far-infrared emission at $24\!-\!500\, \mu$m in the LMC, SMC, M31, and M33. By forward-modelling the point spread function (PSF) on the power spectrum, we find that nearly all power spectra have a single power-law and point source component. A broken power-law model is only favoured for the LMC 24 μm MIPS power spectrum and is due to intense dust heating in 30 Doradus. We also test for local power spectrum variations by splitting the LMC and SMC maps into 820 pc boxes. We find significant variations in the power-law index with no strong evidence for breaks. The lack of a ubiquitous break suggests that the spatial power spectrum does not constrain the disc scale height. This contradicts claims of a break where the turbulent motion changes from 3D to 2D. The power spectrum indices in the LMC, SMC, and M31 are similar (2.0–2.5). M33 has a flatter power spectrum (1.3), similar to more distant spiral galaxies with a centrally-concentrated H2 distribution. We compare the power spectra of H i, CO, and dust in M31 and M33, and find that H i power spectra are consistently flatter than CO power spectra. These results cast doubt on the idea that the spatial power spectrum traces large scale turbulent motion in nearby galaxies. Instead, we find that the spatial power spectrum is influenced by (1) the PSF on scales below ∼3 times the FWHM, (2) bright compact regions (30 Doradus), and (3) the global morphology of the tracer (an exponential CO disc).

Thermal Sunyaev-Zel’dovich anisotropy due to primordial black holes

We investigate the Sunyaev-Zel'dovich (SZ) effect caused by primordial black holes (PBHs) on the cosmic microwave background (CMB) temperature fluctuations. The gas accreting on a PBH heats up by the release of the gravitational energy. As a result, the heated gas in the vicinity of the PBH emits the UV and X-ray photons. These photons can ionize and heat the intergalactic medium (IGM) around the PBH. Assuming the simple model of these emitting photons, we compute the profiles of the IGM ionization fraction and temperature around a PBH. Using these profiles, we evaluate the Compton $y$-parameter created by the IGM gas around a PBH. Finally, we estimate the CMB temperature angular power spectrum due to the PBH SZ effect in our model. We show that the SZ temperature anisotropy due to the PBHs has the flat angular power spectrum on small scale, $l\leq2000$ and could dominate the primordial temperature spectrum on smaller scales than the Silk scale. This flat spectrum extends to the scale of the ionized region by the PBH emission. We also discuss the impact of the small-scale CMB measurement on the PBH abundance based on our results.

Tracking the pre-inflation era from density perturbation spectra

One of the great triumphs of the inflationary model is the prediction of the flat power spectrum of the CMB fluctuation. The prediction is based on the assumption of the de-Sitter vacuum in the past infinity. However, the true past infinity of the inflation is expected to be dominated by radiation and curvature of the space. We consider pre-inflation era as dominated by radiation and curvatures as well as inflation potential. We derive the exact solutions for the scalar fields in this era and find a exact power spectra caused by the inflaton vacuum fluctuation. We show that the power spectrum is almost flat for sub-horizon scale and deviates from flat for very high super-horizon fluctuation, which is quite sensitive to the radiation and the curvature in the pre-inflation era.

Time-delay signature concealed broadband gain-coupled chaotic laser with fiber random grating induced distributed feedback

A broadband chaotic laser with a flat power spectrum extending up to ∼7.53 GHz is achieved by injecting continuous wave laser light into a chaotic diode laser perturbed by fiber random grating induced distributed feedback, which forms a gain-coupled chaotic laser system. More than triple bandwidth enhancement is realized with appropriate frequency detuning between the master and slave lasers. Unlike normal chaotic lasers, the output from such a broadband chaotic laser is free from time-delay signature, which can be potentially applied for practical random number generations and will find useful applications in the fields of information security and computation systems.

Tunable Broadband Chaotic Signal Synthesis From a WRC-FPLD Subject to Filtered Feedback

The synthesis of wavelength-tunable broadband chaotic signals is experimentally demonstrated by using a weak-resonant-cavity Fabry-Perot laser diode (WRC-FPLD) subject to filtered feedback. To perform the broadband tunability from 1544 to 1556 nm, a tunable optical filter is used for providing filtered feedback to drive the laser into chaos. With adjusting the central wavelength of the filter, about 20 longitudinal modes of the WRC-FPLD can individually realize the chaotic output within the tunable range of the filter. Moreover, by suitably selecting the feedback power, the chaos signal with a flat power spectrum and broad bandwidth up to ~30.0 GHz can be achieved.

Temporally correlated fluctuations drive epileptiform dynamics

Macroscopic models of brain networks typically incorporate assumptions regarding the characteristics of afferent noise, which is used to represent input from distal brain regions or ongoing fluctuations in non-modelled parts of the brain. Such inputs are often modelled by Gaussian white noise which has a flat power spectrum. In contrast, macroscopic fluctuations in the brain typically follow a 1/fb spectrum. It is therefore important to understand the effect on brain dynamics of deviations from the assumption of white noise. In particular, we wish to understand the role that noise might play in eliciting aberrant rhythms in the epileptic brain.To address this question we study the response of a neural mass model to driving by stochastic, temporally correlated input. We characterise the model in terms of whether it generates “healthy” or “epileptiform” dynamics and observe which of these dynamics predominate under different choices of temporal correlation and amplitude of an Ornstein-Uhlenbeck process. We find that certain temporal correlations are prone to eliciting epileptiform dynamics, and that these correlations produce noise with maximal power in the δ and θ bands. Crucially, these are rhythms that are found to be enhanced prior to seizures in humans and animal models of epilepsy. In order to understand why these rhythms can generate epileptiform dynamics, we analyse the response of the model to sinusoidal driving and explain how the bifurcation structure of the model gives rise to these findings. Our results provide insight into how ongoing fluctuations in brain dynamics can facilitate the onset and propagation of epileptiform rhythms in brain networks. Furthermore, we highlight the need to combine large-scale models with noise of a variety of different types in order to understand brain (dys-)function.

Bouncing cosmologies in geometries with positively curved spatial sections

Background boucing cosmologies in the framework of General Relativity, driven by a single scalar field filling the Universe, and with a quasi-matter domination period, i.e., depicting the so-called Matter Bounce Scenario, are reconstructed for geometries with positive spatial curvature. These cosmologies lead to a nearly flat power spectrum of the curvature fluctuations in co-moving coordinates for modes that leave the Hubble radius during the quasi-matter domination period, and whose spectral index and its running, which are related with the effective Equation of State parameter given by the quotient of the pressure over the energy density, are compatible with observational data.

A point acoustic device based on aluminum nanowires.

A point Electrical Thermal Acoustic (ETA) device based on aluminum nanowire contacts is designed and fabricated. Interdigitated structural aluminum nanowires are released from the substrate by Inductively Coupled Plasma Reactive Ion Etching (ICP-RIE). By releasing the interdigitated structure, the nanowires contact each other at approximately 1 mm above the wafer, forming a Point Contact Structure (PCS). It is found that the PCS acoustic device realizes high efficiency when a biased AC signal is applied. The PCS acoustic device reaches a sound pressure level as high as 67 dB at a distance of 1 cm with 74 mW AC input. The power spectrum is flat, ranging from 2 kHz to 20 kHz with a less than ±3 dB fluctuation. The highest normalized Sound Pressure Level (SPL) of the point contact structure acoustic device is 18 dB higher than the suspended aluminum wire acoustic device. Comparisons between the PCS acoustic device and the Suspended Aluminum Nanowire (SAN) acoustic device illustrate that the PCS acoustic device has a flatter power spectrum within the 20 kHz range, and enhances the SPL at a lower frequency. Enhancing the response at lower frequencies is extremely useful, which may enable earphone and loudspeaker applications within the frequency range of the human ear with the help of pulse density modulation.

Design of ultralow sidelobe chaotic radar signal by modulating group delay method

This paper proposes a method for chaotic radar signal (CRS) design with ultralow sidelobe performance. We first modulate the group delay (MGD) of a radar signal using a chaotic mapping sequence in the frequency domain, and then we transform the radar signal to its time domain form by inverse Fourier transformation. The designed CRS has ultralow sidelobe owing to its flat power spectrum density (PSD). Meanwhile, its ambiguity function is thumbtack, and the amplitudes of both in-phase and quadrature components are close to Gaussian noise. Both numerical simulation and experimental results demonstrate the ultralow sidelobe performance of the designed CRS.

A LUMINOUS X-RAY FLARE FROM THE NUCLEUS OF THE DORMANT BULGELESS SPIRAL GALAXY NGC 247

NGC 247 is a nearby late-type bulgeless spiral galaxy that contains an inactive nucleus. We report a serendipitous discovery of an X-ray flare from the galaxy center with a luminosity up to 2*10^39 erg/s in the 0.3-10 keV band with XMM-Newton. A Chandra observation confirms that the new X-ray source is spatially coincident with the galaxy nucleus. The XMM-Newton data revealed a hard power-law spectrum with a spectral break near 3-4 keV, no pulsations on timescales longer than 150 ms, and a flat power spectrum consistent with Poisson noise from 1 mHz to nearly 10 Hz. Follow-up observations with Swift detected a second flux peak followed by a luminosity drop by factor of almost 20. The spectral and temporal behaviors of the nuclear source are well consistent with the scenario that the flare was due to an outburst of a low-mass X-ray binary that contains a stellar-mass black hole emitting near its Eddington limit at the peak. However, it cannot be ruled out that the sudden brightening in the nucleus was due to accretion onto a possible low-mass nuclear black hole, fed by a tidally disrupted star or a gas cloud; the MAXI observations limit the peak luminosity of the flare to less than ~10^43 erg/s, suggesting that it is either a low mass black hole or an inefficient tidal disruption event (TDE).