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We present transition probabilities for 268 spectral lines of singly ionized chromium (Cr ii) in the wavelength region 208–414 nm. Branching fractions were measured in archival Fourier transform spectra of chromium-argon and chromium-neon hollow cathode lamps and a Penning discharge source. The branching fractions were combined with previously published experimental lifetimes of 14 levels, and with lifetimes from semiempirical calculations for 14 levels to give transition probabilities. The estimated uncertainties of the transition probabilities range from 10% to 26%. A comparison with previously published experimental transition probabilities shows discrepancies of up to a factor of 2.5 for lines around 213 nm. [ABSTRACT FROM AUTHOR]

The Fourier transformation is an effective and efficient operation of Gaussianization at the one-point level. Using a set of N -body simulation data, we verified that the one-point distribution functions of the dark matter momentum divergence and density fields closely follow complex Gaussian distributions. The one-point distribution function of the quotient of two complex Gaussian variables is introduced and studied. Statistical theories are then applied to model one-point statistics about the growth of individual Fourier modes of the dark matter density field, which can be obtained by the ratio of two Fourier-transformed cosmic fields. Our simulation results proved that the models based on the Gaussian approximation are impressively accurate, and our analysis revealed many interesting aspects of the growth of dark matter’s density fluctuation in Fourier space. [ABSTRACT FROM AUTHOR]

The possibility to compute nucleon electromagnetic form factors in the time-like region by analytic continuation of their space-like expressions, obtained in the framework of a generic model of nucleons, has been explored. We have developed a procedure to analytically solve Fourier transforms of the nucleon electromagnetic current and hence to obtain form factors defined in all kinematic regions and fulfilling the first-principles requirements of analyticity and unitarity. The results obtained in the particular case of the Skyrme model are discussed and compared to data, both in the space-like and time-like region. [ABSTRACT FROM AUTHOR]

According to the properties of Fourier transform, Fourier single-pixel imaging uses the illumination lights with cosine distributions to obtain the Fourier spectrum of the object, and then apply the inverse Fourier transform to reconstruct the spatial information of the object. This technique does not require detector arrays, such as charge coupled device and has proven to be insensitive to distortion, which is a great improvement over traditional photography techniques. In this manuscript, we present a detailed analysis and discussion on the signal-to-noise ratio (SNR) of Fourier single-pixel imaging. Compared with conventional imaging whose SNR is independent of pixel number N, Fourier single-pixel imaging achieves an improved SNR which is up to N times as high as the dynamic range of detection. Furthermore, this SNR benefit is further confirmed experimentally, in cases of one dimension and two dimensions. [ABSTRACT FROM AUTHOR]

Cosmic ray (CR) diurnal anisotropy and Forbush decreases (FDs), as well as the relationship between them, have received considerable study. Several astrophysicists have focused on the speculated impact of FDs on the amplitude of the diurnal CR variations on different timescales. In an attempt to disentangle the contribution of FDs, days of Forbush events are traditionally excluded while calculating the diurnal amplitude in individual neutron monitor (NM) data. But the implications of CR diurnal anisotropy on the magnitude of FDs are rarely investigated in detail. Recently, an effort was made, using a combination of Fast Fourier transform and FD-location algorithms, to account for the contribution of CR diurnal anisotropy on the number, magnitude, and timing of FDs. With some technical advancements, the efficiency of the software is tested in the current work using CR data measured by the oldest CR observatory (Climax) from 1953 to 2006. We find strong and statistically significant correlations between FD magnitude calculated from raw and Fourier transformed CR data and the amplitude of diurnal anisotropy. The relationship is stronger in the case of the Fourier transformed signal, lending credence to the idea that CR anisotropy is a part of Forbush events. In order to validate the observed relationship between the amplitude of CR diurnal variations, magnitude, and timing of FDs, large volumes of data from the Moscow, McMurdo, and Potchefstroom NMs were also analyzed. The significant CR intensity decreases (FD magnitude >5%) at the four stations were ranked according to their magnitudes. [ABSTRACT FROM AUTHOR]

Sample selection is a necessary preparation for weak lensing measurement. It is well-known that selection itself may introduce bias to the measured shear signal. Using image simulation and the Fourier_Quad shear measurement pipeline, we quantify the selection bias in various commonly used selection criteria (signal-to-noise ratio, magnitude, etc.). We propose a new selection criterion defined in the power spectrum of the galaxy image. This new selection criterion has a low selection bias, and it is particularly convenient for shear measurement pipelines based on Fourier transformation. [ABSTRACT FROM AUTHOR]

Diamond quantum processors consisting of a nitrogen-vacancy centre and surrounding nuclear spins have been the key to significant advancements in room-temperature quantum computing, quantum sensing and microscopy. The optimisation of these processors is crucial for the development of large-scale diamond quantum computers and the next generation of enhanced quantum sensors and microscopes. Here, we present a full model of multi-qubit diamond quantum processors and develop a semi-analytical method for designing gate pulses. This method optimises gate speed and fidelity in the presence of random control errors and is readily compatible with feedback optimisation routines. We theoretically demonstrate infidelities approaching ∼10−5 for single-qubit gates and established evidence that this can also be achieved for a two-qubit CZ gate. Consequently, our method reduces the effects of control errors below the errors introduced by hyperfine field misalignment and the unavoidable decoherence that is intrinsic to the processors. Having developed this optimal control, we simulated the performance of a diamond quantum processor by computing quantum Fourier transforms. We find that the simulated diamond quantum processor is able to achieve fast operations with low error probability. [ABSTRACT FROM AUTHOR]

We observed the dynamical evolution of the electron–nuclear wavepacket composed of the and 32Πu states of with an evolution period of 1.3 fs. We created a dissociative wavepacket of by photoionization of O2 with the irradiation of an intense attosecond pulse train (APT) in the extreme ultraviolet (XUV) wavelength region, and probed it with another XUV APT by scanning delay between the two APTs. We revealed the evolution of the electron–nuclear wavepacket by the analysis of the spectral phase in the Fourier transform of the recorded delay dependent momentum spectrum of O+. We also found the correlation between the photon energy and the released kinetic energy originating from the dissociation of Rydberg states of O2 followed by the autoionization of the fragment O atom in the Rydberg states. [ABSTRACT FROM AUTHOR]

Rotation measure synthesis allows the estimation of Faraday dispersion via a Fourier transform and is the primary tool to probe cosmic magnetic fields. We show this can be considered mathematically equivalent to the one-dimensional (1D) interferometric intensity measurement equation, albeit in a different Fourier space. As a result, familiar concepts in 2D intensity interferometry designed to correctly account for a range of instrumental conditions can be translated to the analysis of Faraday dispersion. In particular, we show how to model the effect of channel averaging during Faraday reconstruction, which has to date limited the progress of polarimetric science using wide-band measurements. Further, we simulate 1D sparse reconstruction with channel averaging for realistic frequency coverages, and show that it is possible to recover signals with large rotation measure values that were previously excluded from possible detection. This is especially important for low-frequency and wide-band polarimetry. We extended these ideas to introduce mosaicking in Faraday depth into the channel-averaging process. This work thus provides the first framework for correctly undertaking wide-band rotation measure synthesis, including the provision to add data from multiple telescopes, a prospect that should vastly improve the quality and quantity of polarimetric science. This is of particular importance for extreme environments that generate high magnetic fields such as those associated with pulsars and fast radio bursts, and will allow such sources to be accurately used as probes of cosmological fields. [ABSTRACT FROM AUTHOR]

Variational hybrid quantum-classical algorithms (VHQCAs) are near-term algorithms that leverage classical optimization to minimize a cost function, which is efficiently evaluated on a quantum computer. Recently VHQCAs have been proposed for quantum compiling, where a target unitary U is compiled into a short-depth gate sequence V. In this work, we report on a surprising form of noise resilience for these algorithms. Namely, we find one often learns the correct gate sequence V (i.e. the correct variational parameters) despite various sources of incoherent noise acting during the cost-evaluation circuit. Our main results are rigorous theorems stating that the optimal variational parameters are unaffected by a broad class of noise models, such as measurement noise, gate noise, and Pauli channel noise. Furthermore, our numerical implementations on IBM's noisy simulator demonstrate resilience when compiling the quantum Fourier transform, Toffoli gate, and W-state preparation. Hence, variational quantum compiling, due to its robustness, could be practically useful for noisy intermediate-scale quantum devices. Finally, we speculate that this noise resilience may be a general phenomenon that applies to other VHQCAs such as the variational quantum eigensolver. [ABSTRACT FROM AUTHOR]

The recent breakthrough in metamaterial-based optical computing devices (2014 Science 343 160) has inspired a quest for similar systems in acoustics, performing mathematical operations on sound waves. So far, acoustic analog computing has been demonstrated using thin planar metamaterials, carrying out the operator of choice in Fourier domain. These so-called filtering metasurfaces, however, are always accompanied with additional Fourier transform sub-blocks, enlarging the computing system and preventing its applicability in miniaturized architectures. Here, employing a simple high-index acoustic slab waveguide, we propose a highly compact and potentially integrable acoustic computing system and demonstrate its proper functioning by numerical simulations. The system directly performs mathematical operation in spatial domain and is therefore free of any Fourier bulk lens. Such compact computing system is highly promising for various applications including high throughput image processing, ultrafast equation solving, and real time signal processing. [ABSTRACT FROM AUTHOR]

Quantum computers hold the promise to solve certain problems exponentially faster than their classical counterparts. Trapped atomic ions are among the physical systems in which building such a computing device seems viable. In this work we present a small-scale quantum information processor based on a string of 40Ca+ ions confined in a macroscopic linear Paul trap. We review our set of operations which includes non-coherent operations allowing us to realize arbitrary Markovian processes. In order to build a larger quantum information processor it is mandatory to reduce the error rate of the available operations which is only possible if the physics of the noise processes is well understood. We identify the dominant noise sources in our system and discuss their effects on different algorithms. Finally we demonstrate how our entire set of operations can be used to facilitate the implementation of algorithms by examples of the quantum Fourier transform and the quantum order finding algorithm. [ABSTRACT FROM AUTHOR]

We present a theoretical analysis of the standing wave patterns in scanning tunneling microscope (STM) images, which occur around surface point defects. We consider arbitrary dispersion relations for the surface states and calculate the conductance for a system containing a small-size tunnel contact and a surface impurity. We find rigorous theoretical relations between the interference patterns in the real-space STM images, their Fourier transforms and the Fermi contours of two-dimensional electrons. We propose a new method for reconstructing Fermi contours of surface electron states, directly from the real-space STM images around isolated surface defects. [ABSTRACT FROM AUTHOR]

Electrically conducting films in a time-varying transverse applied magnetic field are considered. Their behavior is strongly influenced by the self-field of the induced currents, making the electrodynamics nonlocal, and consequently difficult to analyze both numerically and analytically.We present a formalism which allows many phenomena related to superconducting and Ohmic films to be modeled and analyzed. The formalism is based on the Maxwell equations and a material current-voltage characteristics, linear for normal metals and nonlinear for superconductors, plus a careful account of the boundary conditions. For Ohmic films, we consider the response to a delta function sourcefield turned on instantly. As one of few problems in nonlocal electrodynamics, this has an analytical solution, which we obtain in both Fourier and real space. Next, the dynamical behavior of a square superconductor film during ramping up of the field, and subsequently returning to zero, is treated numerically. Then, this remanent state is used as initial condition for triggering thermomagnetic avalanches. The avalanches tend to invade the central part where the density of trapped flux is largest, forming dendritic patterns in excellent agreement with magneto-optical images. Detailed profiles of current and flux density are presented and discussed. Finally, the formalism is extended to multiply connected samples, and numerical results for a patterned superconducting film, a ring with a square lattice of antidots, are presented and discussed. [ABSTRACT FROM AUTHOR]

We present low-temperature transport experiments on Aharonov-Bohm (AB) rings fabricated from two-dimensional hole gases in p-type GaAs/AlGaAs heterostructures. Highly visible h/e (up to 15%) and h/2e oscillations, present for different gate voltages, prove the high quality of the fabricated devices. Like in previous work, a clear beating pattern of the h/e and h/2e oscillations is present in the magnetoresistance, producing split peaks in the Fourier spectrum. The magnetoresistance evolution is presented and discussed as a function of temperature and gate voltage. It is found that sample specific properties have a pronounced influence on the observed behaviour. For example, the interference of different transverse modes or the interplay between h/e oscillations and conductance fluctuations can produce the features mentioned above. In previous work they have occasionally been interpreted as signatures of spin-orbit interaction (SOI)-induced effects. In the light of these results, the unambiguous identification of SOI-induced phase effects in AB rings remains still an open and challenging experimental task. [ABSTRACT FROM AUTHOR]

The generator coordinatemethod in the Gaussian overlap approximation (GOA) is applied to a description of the nuclear quadrupole collective states. The full five-dimensional quadrupole tensor is used as a set of the generator coordinates. The integral Hill-Wheeler equation is reduced to a differential equation by using the Fourier transforms of the overlap and energy kernels. The differential Bohr Hamiltonian obtained this way is compared with that derived by the usual approach to the collective Hamiltonian in the GOA which does contain an additional approximation. The method of calculating the quantities which determine the Bohr Hamiltonian from the set of deformation-dependent intrinsic states is demonstrated. In particular, it appears that the moments of inertia at the quadrupole rotations are of the Yoccoz type. [ABSTRACT FROM AUTHOR]

We present spatially resolved observations of the canonical transition disk object TW Hya at 8.74 µm, 11.66 µm, and 18.30 µm, obtained with the T-ReCS instrument on the Gemini telescope. These observations are a result of a novel observing mode at Gemini that enables speckle imaging. Using this technique, we image our target with short enough exposure times to achieve diffraction limited images. We use Fourier techniques to reduce our data, which allows high-precision calibration of the instrumental point-spread function. Our observations span two epochs and we present evidence for temporal variability at 11.66 µm in the disk of TW Hya. We show that previous models of TW Hya's disk from the literature are incompatible with our observations and construct a model to explain the discrepancies. We detect marginal asymmetry in our data, most significantly at the shortest wavelengths. To explain our data, we require a model that includes an optically thin inner disk extending from 0.02 to 3.9AU, an optically thick ring representing the outer disk wall at 3.9AU and extending to 4.6AU, and a hotter-than-disk-equilibrium source of emission located at ~3.5AU. [ABSTRACT FROM AUTHOR]

Recently, there have been significant new insights concerning the conditions under which closed systems equilibrate locally. The question of whether subsystems thermalize-if the equilibrium state is independent of the initial state-is, however, much harder to answer in general. Here, we consider a setting in which thermalization can be addressed: a quantum quench under a Hamiltonian whose spectrum is fixed and whose basis is drawn from the Haar measure. If the Fourier transform of the spectral density is small, almost all bases lead to local equilibration to the thermal state with infinite temperature. This allows us to show that, under almost all Hamiltonians that are unitarily equivalent to a local Hamiltonian, it takes an algebraically small time for subsystems to thermalize. [ABSTRACT FROM AUTHOR]

Direct visualization of electronic-structure symmetry within each crystalline unit cell is a new technique for complex electronic matter research (Lawler et al 2010 Nature 466 347-51, Schmidt et al 2011 New J. Phys. 13 065014, Fujita K et al 2012 J. Phys. Soc. Japan 81 011005). By studying the Bragg peaks in Fourier transforms of electronic structure images and particularly by resolving both the real and imaginary components of the Bragg amplitudes, distinct types of intra-unit-cell symmetry breaking can be studied. However, establishing the precise symmetry point of each unit cell in real space is crucial in defining the phase for such a Bragg-peak Fourier analysis. Exemplary of this challenge is the high-temperature superconductor Bi2Sr2CaCu2O8+δ for which the surface Bi atom locations are observable, while it is the invisible Cu atoms that define the relevant CuO2 unit-cell symmetry point. Here we demonstrate, by imaging with picometer precision the electronic impurity states at individual Zn atoms substituted at Cu sites, that the phase established using the Bi lattice produces a ~2%(2π) error relative to the actual Cu lattice. Such a phase assignment error would not diminish reliability in the determination of intra-unitcell rotational symmetry breaking at the CuO2 plane (Lawler et al 2010 Nature 466 347-51, Schmidt et al 2011 New J. Phys. 13 065014, Fujita K et al 2012 J. Phys. Soc. Japan 81 011005). Moreover, this type of impurity atom substitution at the relevant symmetry site can be of general utility in phase determination for the Bragg-peak Fourier analysis of intra-unit-cell symmetry. [ABSTRACT FROM AUTHOR]

We study the use of a pair of qubits as a decoherence probe of a nontrivial environment. This dual-probe configuration is modelled by three twolevel systems (TLSs), which are coupled in a chain in which the middle system represents an environmental TLS. This TLS resides within the environment of the qubits and therefore its coupling to perturbing fluctuations (i.e. its decoherence) is assumed much stronger than the decoherence acting on the probe qubits. We study the evolution of such a tripartite system including the appearance of a decoherence-free state (dark state) and non-Markovian behaviour. We find that all parameters of this TLS can be obtained from measurements of one of the probe qubits. Furthermore, we show the advantages of two qubits in probing environments and the new dynamics imposed by a TLS that couples to two qubits at once. [ABSTRACT FROM AUTHOR]

We demonstrate an x-ray imaging method that combines Fourier transform holography with tomography ('tomoholography') for threedimensional (3D) microscopic imaging. A 3D image of a diatom shell with a spatial resolution of 140 nm is presented. The experiment is realized by using a small gold sphere as the reference wave source for holographic imaging. This setup allows us to rotate the sample and to collect a number of 2D projections for tomography. [ABSTRACT FROM AUTHOR]

We trace with analytical methods and in a model parameter-independent manner the independent bits of Fisher information of each of the moments of the lognormal distribution as a now standard prescription for the distribution of the cosmological matter density field as it departs from Gaussian initial conditions. We show that, when entering the regime of large fluctuations, only a tiny, dramatically decaying fraction of the total information content remains accessible through the extraction of the full series of moments of the field. This is due to the known peculiarity of highly tailed distributions that they cannot be uniquely recovered given the values of all of their moments. Under this lognormal assumption, cosmological probes such as the correlation function hierarchy or, equivalently, their Fourier transforms, are rendered fundamentally limited once the field becomes nonlinear, for any parameter of interest. We show that the fraction of the information accessible from two-point correlations decays to zero following the inverse squared variance of the field. We discuss what general properties of a random field's probability density function are making the correlation function hierarchy an efficient or inefficient, complete or incomplete, set of probes of any model parameter. [ABSTRACT FROM AUTHOR]

We determine the magnetic helicity, along with the magnetic energy, at high latitudes using data from the Ulysses mission. The data set spans the time period from 1993 to 1996. The basic assumption of the analysis is that the solar wind is homogeneous. Because the solar wind speed is high, we follow the approach first pioneered by Matthaeus et al. by which, under the assumption of spatial homogeneity, one can use Fourier transforms of the magnetic field time series to construct one-dimensional spectra of the magnetic energy and magnetic helicity under the assumption that the Taylor frozen-in-flow hypothesis is valid. That is a well-satisfied assumption for the data used in this study. The magnetic helicity derives from the skew-symmetric terms of the three-dimensional magnetic correlation tensor, while the symmetric terms of the tensor are used to determine the magnetic energy spectrum. Our results show a sign change of magnetic helicity at wavenumber k ≈ 2 AU-1 (or frequency v ≈ 2 μHz) at distances below 2.8 AU and at k ≈ 30 AU-1 (or v ≈ 25 μHz) at larger distances. At small scales the magnetic helicity is positive at northern heliographic latitudes and negative at southern latitudes. The positive magnetic helicity at small scales is argued to be the result of turbulent diffusion reversing the sign relative to what is seen at small scales at the solar surface. Furthermore, the magnetic helicity declines toward solar minimum in 1996. The magnetic helicity flux integrated separately over one hemisphere amounts to about 1045 Mx2 cycle-1 at large scales and to a three times lower value at smaller scales. [ABSTRACT FROM AUTHOR]

Non-equilibrium dynamics of a Lieb-Liniger system in the presence of the hard-wall potential is studied. We demonstrate that a time-dependent wave function, which describes quantum dynamics of a Lieb-Liniger wave packet consisting of N particles, can be found by solving an N-dimensional Fourier transform; this follows from the symmetry properties of the many-body eigenstates in the presence of the hard-wall potential. The presented formalism is employed to numerically calculate reflection of a few-body wave packet from the hard wall for various interaction strengths and incident momenta. [ABSTRACT FROM AUTHOR]

In this paper, we study the optical properties of single defects emitting in the near infrared (NIR) in nanodiamonds at liquid helium temperature. The nanodiamonds are synthesized using a microwave chemical vapor deposition method followed by nickel implantation and annealing. We show that single defects exhibit several striking features at cryogenic temperature: the photoluminescence is strongly concentrated into a sharp zerophonon line (ZPL) in the NIR, the radiative lifetime is in the nanosecond range and the emission is linearly polarized. The spectral stability of the defects is then investigated. An optical resonance linewidth of 4 GHz is measured using resonant excitation on the ZPL. Although Fourier-transform-limited emission is not achieved, our results show that it might be possible to use consecutive photons emitted in the NIR by single defects in diamond nanocrystals to perform two photon interference experiments, which are at the heart of linear quantum computing protocols. [ABSTRACT FROM AUTHOR]

We consider quantum learning machines-quantum computers that modify themselves in order to improve their performance in some way-that are trained to perform certain classical task, i.e. to execute a function that takes classical bits as input and returns classical bits as output. This allows a fair comparison between learning efficiency of quantum and classical learning machines in terms of the number of iterations required for completion of learning. We find an explicit example of the task for which numerical simulations show that quantum learning is faster than its classical counterpart. The task is extraction of the kth root of NOT (NOT = logical negation), with k = 2m and mϵℕ. The reason for this speed-up is that the classical machine requires memory of size log k = m to accomplish the learning, while the memory of a single qubit is sufficient for the quantum machine for any k. [ABSTRACT FROM AUTHOR]

The influence of the coordination on the Kondo temperature of a magnetic impurity at a noble metal surface and the line shape observed in low temperature scanning tunneling spectroscopy (STS) is investigated for single cobalt atoms adsorbed on and embedded in copper surfaces. Surprisingly, the Kondo temperature for substitutional cobalt atoms is almost the same as that of adatoms on the Cu(100) surface. This is in stark contrast to the behaviour observed at the Cu(111) surface. DFT calculations reveal that in the case of Cu(100) the coupling of the spin of the cobalt atom to the conduction band is not substantially increased by the incorporation of the cobalt atom. At the same time the observed line shape differs strongly from what is observed on adatom systems. [ABSTRACT FROM AUTHOR]

A number of elegant approaches have been developed for the identification of quantum circuits which can be efficiently simulated on a classical computer. Recently, these methods have been employed to demonstrate the classical simulability of the quantum Fourier transform (QFT). Here we show that one can demonstrate a number of simulability results for QFT circuits in a straightforward manner using Griffiths and Niu's semi-classical QFT construction (Griffiths and Niu 1996 Phys. Rev. Lett. 76 3228). We use this to analyse the simulability properties of the QFT with a variety of classes of entangled input states. We then discuss the consequences of these results in the context of Shor's factorization algorithm. [ABSTRACT FROM AUTHOR]

Chirped and non-chirped Super Gaussians (SG) are very common in pulse modeling for optical communications. However, unlike Gaussian pulses, the propagation (and distortions) of SG pulses in dispersive media cannot be expressed in closed-form analytical expression, nor can its Fourier transform, i.e. its spectrum. In this paper, it is shown that analytical smooth rectangular can be utilized to formulate analytically (in both time and frequency domains) with high accuracy the propagation of chirped SG pulses in dispersive medium. The paper also elaborates on chirped pulses cascading and on the propagation of asymmetric SG pulses. [ABSTRACT FROM AUTHOR]

We present an efficient method for estimating the eigenvalues of a Hamiltonian H from the expectation values of the evolution operator for various times. For a given quantum state ρ, our method outputs a list of eigenvalue estimates and approximate probabilities. Each probability depends on the support of ρ in those eigenstates of H associated with eigenvalues within an arbitrarily small range. The complexity of our method is polynomial in the inverse of a given precision parameter ϵ, which is the gap between eigenvalue estimates. Unlike the well-known quantum phase estimation algorithm that uses the quantum Fourier transform, our method does not require large ancillary systems, large sequences of controlled operations, or preserving coherence between experiments, and is therefore more attractive for near-term applications. The output of our method can be used to estimate spectral properties of H and other expectation values efficiently, within additive error proportional to ϵ. [ABSTRACT FROM AUTHOR]

We present limits on the 21 cm power spectrum from the Epoch of Reionization using data from the 64 antenna configuration of the Donald C. Backer Precision Array for Probing the Epoch of Reionization (PAPER) analyzed through a power spectrum pipeline independent from previous PAPER analyses. Previously reported results from PAPER have been found to contain significant signal loss. Several lossy steps from previous PAPER pipelines have not been included in this analysis, namely delay-based foreground filtering, optimal fringe-rate filtering, and empirical covariance-based estimators. Steps that remain in common with previous analyses include redundant calibration and local sidereal time (LST) binning. The power spectra reported here are effectively the result of applying a linear Fourier transform analysis to the calibrated, LST-binned data. This analysis also uses more data than previous publications, including the complete available redshift range of z ∼ 7.5 to 11. In previous PAPER analyses, many power spectrum measurements were found to be detections of noncosmological power at levels of significance ranging from two to hundreds of times the theoretical noise. Here, excess power is examined using redundancy between baselines and power spectrum jackknives. The upper limits we find on the 21 cm power spectrum from reionization are , , , , , and at redshifts z = 10.87, 9.93, 8.68, 8.37, 8.13, and 7.48, respectively. For reasons described in Cheng et al., these limits supersede all previous PAPER results. [ABSTRACT FROM AUTHOR]

Foreground power dominates the measurements of interferometers that seek a statistical detection of highly-redshifted H i emission from the Epoch of Reionization (EoR). The chromaticity of the instrument creates a boundary in the Fourier transform of frequency (proportional to k∥) between spectrally smooth emission, characteristic of the strong synchrotron foreground (the “wedge”), and the spectrally structured emission from H i in the EoR (the “EoR window”). Faraday rotation can inject spectral structure into otherwise smooth polarized foreground emission, which through instrument effects or miscalibration could possibly pollute the EoR window. For instruments pursuing a “foreground avoidance” strategy of simply measuring in the EoR window, and not attempting to model and remove foregrounds, as is the plan for the first stage of the Hydrogen Epoch of Reionization Array (HERA), characterizing the intrinsic instrument polarization response is particularly important. Using data from the HERA 19-element commissioning array, we investigate the polarization response of this new instrument in the power-spectrum domain. We perform a simple image-based calibration based on the unpolarized diffuse emission of the Global Sky Model, and show that it achieves qualitative redundancy between the nominally redundant baselines of the array and reasonable amplitude accuracy. We construct power spectra of all fully polarized coherencies in all pseudo-Stokes parameters, and discuss the achieved isolation of foreground power due to the intrinsic spectral smoothness of the foregrounds, the instrument chromaticity, and the calibration. We compare to simulations based on an unpolarized diffuse sky model and detailed electromagnetic simulations of the dish and feed, confirming that in Stokes I, the calibration does not add significant spectral structure beyond that expected from the interferometer array configuration and the modeled primary beam response. Furthermore, this calibration is stable over the 8 days of observations considered. Excess power is seen in the power spectra of the linear polarization Stokes parameters, which is not easily attributable to leakage via the primary beam, and results from some combination of residual calibration errors and actual polarized emission. Stokes V is found to be highly discrepant from the expectation of zero power, strongly pointing to the need for more accurate polarized calibration. [ABSTRACT FROM AUTHOR]

In this paper, we present an analysis of the pulsating behavior of Kepler target KIC 10284901. The Fourier transform of the high-precision light curve reveals seven independent frequencies for its light variations. Among them, the first two frequencies are main pulsation modes: F0 = 18.994054(1) day−1 and F1 = 24.335804(4) day−1; the ratio F0/F1 = 0.7805 classifies this star as a double-mode high-amplitude δ Scuti (HADS) star; another two frequencies, fm1 = 0.4407 day−1 and fm2 = 0.8125 day−1, are detected directly, and the modulations of fm1 and fm2 to F0 and F1 modes (seen as quintuplet structures centered on these two modes in the frequency spectrum) are also found. This is the first detection of a double-modulation effect in the HADS stars. The features of the frequency pattern and the ratio (fm1/fm2 ≈ 1:2), as well as the cyclic variation of amplitude of the two dominant pulsation modes, which seem to be similar to that in Blazhko RR Lyrae stars, indicate this modulation might be related to the Blazhko effect. A preliminary analysis suggests that KIC 10284901 is in the bottom of the HADS instability strip and situated in the main sequence. [ABSTRACT FROM AUTHOR]

Radio interferometers consisting of identical antennas arranged on a regular lattice permit fast Fourier transform beamforming, which reduces the correlation cost from in the number of antennas to . We develop a formalism for describing this process and apply this formalism to derive a number of algorithms with a range of observational applications. These include algorithms for forming arbitrarily pointed tied-array beams from the regularly spaced Fourier transform–formed beams, sculpting the beams to suppress sidelobes while only losing percent-level sensitivity, and optimally estimating the position of a detected source from its observed brightness in the set of beams. We also discuss the effect that correlations in the visibility-space noise, due to cross talk and sky contributions, have on the optimality of Fourier transform beamforming, showing that it does not strictly preserve the sky information of the n2 correlation, even for an idealized array. Our results have applications to a number of upcoming interferometers, in particular the Canadian Hydrogen Intensity Mapping Experiment–Fast Radio Burst (CHIME/FRB) project. [ABSTRACT FROM AUTHOR]

We use two-dimensional Fourier transformation to measure the pitch angle (φ) of the dominant spiral Fourier mode of well-defined spiral arms in 13 protoplanetary disks, making use of near-infrared scattered-light images of AB Aur, SAO 206462, MWC 758, V1247 Ori, HD 142527, DZ Cha, LkHα 330, and HD 100453, and ALMA millimeter continuum images of Elias 2-27, IM Lup, AS 205, and HT Lup. We find that the measured pitch angle correlates strongly with disk mass (MD), such that more massive protoplanetary disks have smaller pitch angles, following . Interestingly, four disks with a known companion (HD 142527, HD 100453, AS 205, and HT Lup) share the same trend. Such a strong dependence of spiral arm pitch angle on disk mass suggests that the disk mass, independent of the formation mechanism, plays a fundamental role in determining the arm tightness of the observed spiral structure. The physical origin of the relation is still not clear. The pitch angle of spiral arms in protoplanetary disks provides an independent constraint on the disk mass. [ABSTRACT FROM AUTHOR]

A general analytical theory of temporal relaxation processes in isolated quantum systems with many degrees of freedom is elaborated, which unifies and substantially amends several previous approximations. Specifically, the Fourier transform of the initial energy distribution is found to play a key role, which is furthermore equivalent to the so-called survival probability in case of a pure initial state. The main prerequisite is the absence of any notable transport currents, caused for instance by some initially unbalanced local densities of particles, energy, and so on. In particular, such a transportless relaxation scenario naturally arises when both the system Hamiltonian and the initial non-equilibrium state do not exhibit any spatial inhomogeneities on macroscopic scales. A further requirement is that the relaxation must not be notably influenced by any approximate (but not exact) constant of motion or metastable state. The theoretical predictions are compared with various experimental and numerical results from the literature. [ABSTRACT FROM AUTHOR]

We provide a detailed analysis of the three-dimensional cross correlation properties of speckle patterns in the deep Fresnel region scattered by random surface. Basing on Kirchhoff approximation, we first derive the quantitative relationship between the longitudinal correlation function and the fractal characteristics of random surface. A novel measuring method is proposed for extracting the roughness exponent of random surface from the longitudinal correlation function of speckles. In experiment, the speckle patterns deviating different distance from the object plane are acquired by a microscopic imaging system. The longitudinal correlation function of the speckles descends with the increase of deviating distance in the form of negative power law. By calculating the Fourier transform of the longitudinal correlation function, we obtain the roughness exponent of random surface by making linear fitting in the large spectrum region. The extracted results are in good agreement with those measured by an atomic force microscopic, which indicate our method has a satisfying accuracy. [ABSTRACT FROM AUTHOR]

Collective scattering of spatially coherent radiation by separated point emitters induces inter-particle forces. For particles close to nano-photonic structures as, for example, nano-fibers, hollow core fibers or photonic waveguides, this pair-interaction induced by monochromatic light is periodic and virtually of infinite range. Here we show that the shape and range of the optical interaction potential can be precisely controlled by spectral design of the incoming illumination. If each particle is only weakly coupled to the confined guided modes the forces acting within a particle ensemble can be decomposed to pairwise interactions. These forces can be tailored to almost arbitrary spatial dependence as they are related to Fourier transforms with coefficients controlled by the intensities and frequencies of the illuminating lasers. We demonstrate the versatility of the scheme by highlighting some examples of unconventional pair potentials. Implementing these interactions in a chain of trapped quantum particles could be the basis of a versatile quantum simulator with almost arbitrary all-to-all interaction control. [ABSTRACT FROM AUTHOR]

We explore the use of principal component analysis (PCA) to characterize high-fidelity simulations and interferometric observations of the millimeter emission that originates near the horizons of accreting black holes. We show mathematically that the Fourier transforms of eigenimages derived from PCA applied to an ensemble of images in the spatial domain are identical to the eigenvectors of PCA applied to the ensemble of the Fourier transforms of the images, which suggests that this approach may be applied to modeling the sparse interferometric Fourier-visibilities produced by an array such as the Event Horizon Telescope. We also show that the simulations in the spatial domain can themselves be compactly represented with a PCA-derived basis of eigenimages, which allows for detailed comparisons to be made between variable observations and time-dependent models, as well as for detection of outliers or rare events within a time series of images. Furthermore, we demonstrate that the spectrum of PCA eigenvalues is a diagnostic of the power spectrum of the structure and, hence, of the underlying physical processes in the simulated and observed images. [ABSTRACT FROM AUTHOR]

We study the Wigner crystallization on partially filled topological flat bands of kagome, honeycomb and checkerboard lattices. We identify the Wigner crystals (WCs) by analyzing the Cartesian and angular Fourier transform of the pair correlation density of the many-body ground state obtained using exact diagonalization. The crystallization strength, measured by the magnitude of the Fourier peaks, increases with decreasing particle density. The Wigner crystallization observed by us is a robust and general phenomenon, existing in all three lattice models for a broad range of filling factors and interaction parameters. The shape of the resulting WCs is determined by the boundary conditions of the chosen plaquette. It is to a large extent independent on the underlying lattice, including its topology, and follows the behavior of classical point particles. [ABSTRACT FROM AUTHOR]

One of the key issues in unraveling the mystery of high TC superconductivity in the cuprates is to understand the normal state outside the superconducting dome. Here we perform scanning tunneling microscopy and spectroscopy measurements on a heavily overdoped, non-superconducting (Bi, Pb)2Sr2CuO6+δ cuprate. Spectroscopic imaging reveals dispersive quasiparticle interferences (QPIs) and the Fourier transforms uncover the evolution of momentum space topology. More interestingly, we observe nanoscale patches of static charge order with periodicity. Both the dispersive QPI and static charge order can be qualitatively explained by theoretical calculations, which reveal the unique electronic structure of strongly overdoped cuprate. [ABSTRACT FROM AUTHOR]

A critical challenge in the observation of the redshifted 21 cm line is its separation from bright Galactic and extragalactic foregrounds. In particular, the instrumental leakage of polarized foregrounds, which undergo significant Faraday rotation as they propagate through the interstellar medium, may harmfully contaminate the 21 cm power spectrum. We develop a formalism to describe the leakage due to instrumental widefield effects in visibility-based power spectra measured with redundant arrays, extending the delay-spectrum approach presented in Parsons et al. We construct polarized sky models and propagate them through the instrument model to simulate realistic full-sky observations with the Precision Array to Probe the Epoch of Reionization. We find that the leakage due to a population of polarized point sources is expected to be higher than diffuse Galactic polarization at any k mode for a 30 m reference baseline. For the same reference baseline, a foreground-free window at k > 0.3 h Mpc−1 can be defined in terms of leakage from diffuse Galactic polarization even under the most pessimistic assumptions. If measurements of polarized foreground power spectra or a model of polarized foregrounds are given, our method is able to predict the polarization leakage in actual 21 cm observations, potentially enabling its statistical subtraction from the measured 21 cm power spectrum. [ABSTRACT FROM AUTHOR]

Eccentric binaries known as heartbeat stars experience strong dynamical tides as the stars pass through periastron, providing a laboratory to study tidal interactions. We measure the rotation periods of 24 heartbeat systems, using the Kepler light curves to identify rotation peaks in the Fourier transform. Where possible, we compare the rotation period to the pseudosynchronization period derived by Hut. Few of our heartbeat stars are pseudosynchronized with the orbital period. For four systems, we were able to identify two sets of rotation peaks, which we interpret as the rotation from both stars in the binary. Most stars in our sample have rotation rates larger than the pseudosynchronization period while a single target rotates much faster than this rate. The majority of the systems have a rotation period that is approximately times the pseudosynchronization period, suggesting that other physical mechanisms strongly influence the star’s evolution. [ABSTRACT FROM AUTHOR]

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform of finely binned galaxy positions. In both cases, deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multipoint hierarchy. We identify some threads of modern large-scale inference methodology that will presumably yield detections in new wider and deeper surveys. [ABSTRACT FROM AUTHOR]

Image coaddition is one of the most basic operations that astronomers perform. In Paper I, we presented the optimal ways to coadd images in order to detect faint sources and to perform flux measurements under the assumption that the noise is approximately Gaussian. Here, we build on these results and derive from first principles a coaddition technique that is optimal for any hypothesis testing and measurement (e.g., source detection, flux or shape measurements, and star/galaxy separation), in the background-noise-dominated case. This method has several important properties. The pixels of the resulting coadded image are uncorrelated. This image preserves all the information (from the original individual images) on all spatial frequencies. Any hypothesis testing or measurement that can be done on all the individual images simultaneously, can be done on the coadded image without any loss of information. The PSF of this image is typically as narrow, or narrower than the PSF of the best image in the ensemble. Moreover, this image is practically indistinguishable from a regular single image, meaning that any code that measures any property on a regular astronomical image can be applied to it unchanged. In particular, the optimal source detection statistic derived in Paper I is reproduced by matched filtering this image with its own PSF. This coaddition process, which we call proper coaddition, can be understood as the maximum signal-to-noise ratio measurement of the Fourier transform of the image, weighted in such a way that the noise in the entire Fourier domain is of equal variance. This method has important implications for multi-epoch seeing-limited deep surveys, weak lensing galaxy shape measurements, and diffraction-limited imaging via speckle observations. The last topic will be covered in depth in future papers. We provide an implementation of this algorithm in MATLAB. [ABSTRACT FROM AUTHOR]

We present a numerical and analytical study of incompressible homogeneous conducting fluids using a helical Fourier representation. We analytically study both small- and large-scale dynamo properties, as well as the inverse cascade of magnetic helicity, in the most general minimal subset of interacting velocity and magnetic fields on a closed Fourier triad. We mainly focus on the dependency of magnetic field growth as a function of the distribution of kinetic and magnetic helicities among the three interacting wavenumbers. By combining direct numerical simulations of the full magnetohydrodynamics equations with the helical Fourier decomposition, we numerically confirm that in the kinematic dynamo regime the system develops a large-scale magnetic helicity with opposite sign compared to the small-scale kinetic helicity, a sort of triad-by-triad α-effect in Fourier space. Concerning the small-scale perturbations, we predict theoretically and confirm numerically that the largest instability is achived for the magnetic component with the same helicity of the flow, in agreement with the Stretch–Twist–Fold mechanism. Vice versa, in the presence of Lorentz feedback on the velocity, we find that the inverse cascade of magnetic helicity is mostly local if magnetic and kinetic helicities have opposite signs, while it is more nonlocal and more intense if they have the same sign, as predicted by the analytical approach. Our analytical and numerical results further demonstrate the potential of the helical Fourier decomposition to elucidate the entangled dynamics of magnetic and kinetic helicities both in fully developed turbulence and in laminar flows. [ABSTRACT FROM AUTHOR]

Astronomical radio signals are subjected to phase dispersion while traveling through the interstellar medium. To optimally detect a short-duration signal within a frequency band, we have to precisely compensate for the unknown pulse dispersion, which is a computationally demanding task. We present the “fast dispersion measure transform” algorithm for optimal detection of such signals. Our algorithm has a low theoretical complexity of , where Nf, Nt, and NΔ are the numbers of frequency bins, time bins, and dispersion measure bins, respectively. Unlike previously suggested fast algorithms, our algorithm conserves the sensitivity of brute-force dedispersion. Our tests indicate that this algorithm, running on a standard desktop computer and implemented in a high-level programming language, is already faster than the state-of-the-art dedispersion codes running on graphical processing units (GPUs). We also present a variant of the algorithm that can be efficiently implemented on GPUs. The latter algorithm’s computation and data-transport requirements are similar to those of a two-dimensional fast Fourier transform, indicating that incoherent dedispersion can now be considered a nonissue while planning future surveys. We further present a fast algorithm for sensitive detection of pulses shorter than the dispersive smearing limits of incoherent dedispersion. In typical cases, this algorithm is orders of magnitude faster than enumerating dispersion measures and coherently dedispersing by convolution. We analyze the computational complexity of pulsed signal searches by radio interferometers. We conclude that, using our suggested algorithms, maximally sensitive blind searches for dispersed pulses are feasible using existing facilities. We provide an implementation of these algorithms in Python and MATLAB. [ABSTRACT FROM AUTHOR]

We study the incommensurate charge ordered states in the model using the Gutzwiller mean field theory on large systems. In particular, we explore the properties of incommensurate charge modulated states referred to as nodal pair density waves (nPDW) in the literature. nPDW states intertwine site and bond charge order with modulated d-wave pair order, and are characterized by a nonzero amplitude of uniform pairing; they also manifest a dominant intra-unit cell d-density wave form factor. To compare with a recent scanning tunneling microscopy (STM) study (Hamidian et al 2015 Nat. Phys.12 150) of the cuprate superconductor BSCCO-2212, we compute the continuum local density of states (LDOS) at a typical STM tip height using the Wannier function based approach. By Fourier transforming Cu and O sub-lattice LDOS we also obtain bias-dependent intra-unit cell form factors and spatial phase difference. We find that in the nPDW state the behavior of form factors and spatial phase difference as a function of energy agrees remarkably well with the experiment.This is in contrast to commensurate charge modulated states, which we show do not agree with experiment. We propose that the nPDW states are good candidates for the charge density wave phase observed in the superconducting state of underdoped cuprates. [ABSTRACT FROM AUTHOR]

We study the possibility of using quadrupole moments of auto-convolved galaxy images to measure cosmic shear. The autoconvolution of an image corresponds to the inverse Fourier transformation of its power spectrum. The new method has the following advantages: the smearing effect due to the point-spread function (PSF) can be corrected by subtracting the quadrupole moments of the auto-convolved PSF; the centroid of the auto-convolved image is trivially identified; the systematic error due to noise can be directly removed in Fourier space; the PSF image can also contain noise, the effect of which can be similarly removed. With a large ensemble of simulated galaxy images, we show that the new method can reach a sub-percent level accuracy under general conditions, albeit with increasingly large stamp size for galaxies of less compact profiles. [ABSTRACT FROM AUTHOR]

Electronic wave functions of planar molecules can be reconstructed via inverse Fourier transform of angle-resolved photoelectron spectroscopy (ARPES) data, provided the phase of the electron wave in the detector plane is known. Since the recorded intensity is proportional to the absolute square of the Fourier transform of the initial state wave function, information about the phase distribution is lost in the measurement. It was shown that the phase can be retrieved in some cases by iterative algorithms using a priori information about the object such as its size and symmetry. We suggest a more generalized and robust approach for the reconstruction of molecular orbitals based on state-of-the-art phase-retrieval algorithms currently used in coherent diffraction imaging (CDI). We draw an analogy between the phase problem in molecular orbital imaging by ARPES and of that in optical CDI by performing an optical analogue experiment on micrometer-sized structures. We successfully reconstruct amplitude and phase of both the micrometer-sized objects and a molecular orbital from the optical and photoelectron far-field intensity distributions, respectively, without any prior information about the shape of the objects. [ABSTRACT FROM AUTHOR]