Spatial-temporal Correlation Functions Research Articles

Hierarchical generalization of dual unitarity

Quantum dynamics with local interactions in lattice models display rich physics, but is notoriously hard to study. Dual-unitary circuits allow for exact answers to interesting physical questions in clean or disordered one- and higher-dimensional quantum systems. However, this family of models shows some non-universal features, like vanishing correlations inside the light-cone and instantaneous thermalization of local observables. In this work we propose a generalization of dual-unitary circuits where the exactly calculable spatial-temporal correlation functions display richer behavior, and have non-trivial thermalization of local observables. This is achieved by generalizing the single-gate condition to a hierarchy of multi-gate conditions, where the first level recovers dual-unitary models, and the second level exhibits these new interesting features. We also extend the discussion and provide exact solutions to correlators with few-site observables and discuss higher-orders, including the ones after a quantum quench. In addition, we provide exhaustive parametrizations for qubit cases, and propose a new family of models for local dimensions larger than two, which also provides a new family of dual-unitary models.

3D geometry‐based UAV to vehicle multiple‐input multiple‐output channel model incorporating Unmanned aerial vehicle heaving motion

AbstractUnmanned aerial vehicles (UAVs) play a vital role in the beyond fifth‐generation (B5G) and sixth‐generation (6G) wireless communication scenarios. This paper proposes a non‐stationary three‐dimensional (3D) geometry‐based multiple‐input multiple‐output channel model for UAV to vehicle (U2V) communications considering UAV heaving motion. The proposed model incorporates the effects of UAV heaving along with the rotation, acceleration, and 3D velocity variation for matching the realistic U2V communication scenarios. The computation methods for time variant channel parameters such as Doppler frequencies, angle of arrival, and angle of departure are given and analysed. The theoretical and statistical properties, including spatial temporal correlation function, TCF, level crossing rate, average fade duration, and Doppler power spectral density are derived and analysed aiming to evaluate the proposed model. Simulation results show that the output statistical characteristics agree with the hypothetical and simulated outcomes, which shows the validity of both the channel model and theoretical derivations.The cover image is based on the Research Article 3D geometry‐based UAV to vehicle multiple‐input multiple‐output channel model incorporating Unmanned aerial vehicle heaving motion by Naeem Ahmed et al., https://doi.org/10.1049/mia2.12393

Correcting Deviations of Emulated Spatial Correlation for Prefaded Signal Synthesis Method With Limited Number of Random Drops in MIMO OTA Testing

The prefaded signals synthesis (PFS) is a well-established over-the-air (OTA) testing solution, which can reconstruct the desired spatial profiles of the target channel by adjusting the power weights of the multiple probes. However, practical channel emulation campaigns tend to use a limited number of random drops due to limited time budget and hardware capacity constraint, which may cause the emulated spatial correlation to be deviated from the expected one due to the loss of ergodicity. In this article, the properties of the emulated channel under the PFS method are reexamined for a given set of initial subpath phases that are randomly configured at different probes. The analytical expressions of the spatial–temporal correlation function (STCF) are thus derived by averaging over time, compared with the general manipulations of ensemble averaging in the literature. Our derivations indicate that the spatial correlation function (SCF) of the emulated channel may deviate from the expected form for a given set of initial subpath phases in the classic PFS method. An improved configuration method for initial subpath phases is proposed. Simulation results show that the proposed method can reproduce the exact SCF in any random drop while unaffecting other important channel properties, for example, the temporal correlation function (TCF).

Channel Characterization for Hyperloops Using the Nonstationary Geometry-Based Model

As a novel means of high-speed transportation, the Hyperloop can proceed at an ultra-high speed (more than 1000 km/h) in the long and narrow pipelines. In this paper, the channel characteristic of the Hyperloop wireless communication systems is the main objective. Based on the geometric scattering theories, a novel nonstationary channel model is proposed to investigate the channel characteristics for Hyperloop train-to-ground communications. According to this model, the channel impulse response (CIR) is obtained, and the closed-form expressions of the multi-link spatial-temporal correlation functions, including the spatial cross-correlation function (CCF) and the temporal autocorrelation function (ACF) are derived and analyzed. Simulation results show that a high correlation between the multi-link channels in vacuum tube scenario can be observed. The relevant research results will contribute to the design of future Hyperloop wireless communication system.

A General 3D Nonstationary Vehicle-to-Vehicle Channel Model Allowing 3D Arbitrary Trajectory and 3D-Shaped Antenna Array

Most of the existing channel model for multiple-input multiple-output (MIMO) vehicle-to-vehicle (V2V) communications only considered that the terminals were equipped with linear antenna arrays and moved with fixed velocities. Nevertheless, under the realistic environment, those models are not practical since the velocities and trajectories of mobile transmitter (MT) and mobile receiver (MR) could be time-variant and unpredictable due to the complex traffic conditions. This paper develops a general 3D nonstationary V2V channel model, which is based on the traditional geometry-based stochastic models (GBSMs) and the twin-cluster approach. In contrast to the traditional models, this new model is characterized by 3D scattering environments, 3D antenna arrays, and 3D arbitrary trajectories of both terminals and scatterers. The calculating methods of channel parameters are also provided. In addition, the statistical properties, i.e., spatial-temporal correlation function (STCF) and Doppler power spectrum density (DPSD), are derived in detail. Simulation results have demonstrated that the output statistical properties of the proposed model agree well with the theoretical and measured results, which verifies the effectiveness of theoretical derivations and channel model as well.

A Novel 3D Non-Stationary Vehicle-to-Vehicle Channel Model and its Spatial-Temporal Correlation Properties

In this paper, a new non-stationary Vehicle-to-Vehicle (V2V) channel model is proposed. It could generate more smooth fading phase between the adjacent channel states and guarantee more accurate Doppler frequency, which is a great improvement comparing with those of the existing non-stationary geometry-based stochastic models (GBSMs) for V2V channels. Meanwhile, the spatial–temporal correlation function (STCF) as well as a temporal correlation function (TCF) and a spatial correlation function (SCF) are derived in details based on the power angle spectrums of both the mobile transmitter (MT) and mobile receiver (MR) following the Von Mises Fisher (VMF) distribution. Simulation results have demonstrated that the time-variant correlation properties of our proposed channel model have an excellent agreement with the theoretical results, which verifies the correctness of theoretical derivations and simulations. Finally, the TCF and stationary interval of the proposed model are verified by the measured results.

Cross-frequency coherence and pulse propagation in a turbulent atmosphere.

Cross-frequency coherence of acoustic signals in a turbulent atmosphere is an important consideration for source localization with acoustic sensor arrays and for remote sensing of the atmosphere with sodars and tomography techniques. This paper takes as a starting point recently derived, closed-form equations for the spatial-temporal correlation function of a broadband acoustic signal propagating in a turbulent atmosphere with coupled spatial-temporal fluctuations in temperature and wind velocity. This theory is employed to calculate, based on the Rytov approximation, the two-point, two-time, two-frequency mutual coherence function of plane and spherical waves in the weak scattering regime. The cross-frequency coherence for these waveforms is then obtained and compared with that in the geometrical acoustics approximation. The coherence bandwidth is calculated and analyzed for typical meteorological regimes of the atmospheric surface layer and parameters of sound propagation. The results obtained are compared with available experimental data. The cross-frequency coherence is also used to study the effect of atmospheric turbulence on the mean intensity of an acoustic pulse propagating in a turbulent atmosphere.

Pulse scattering in a turbulent atmosphere with applications to acoustic remote sensing of the atmosphere with sodars

A new, rigorous theory of acoustic pulse scattering in a turbulent atmosphere with spatial-temporal fluctuations in temperature and wind velocity is developed. The theory generalizes the classical theory of sound scattering to broadband signals and coupled spatial-temporal fluctuations of random fields. The scattered sound field is obtained as a Born approximation of a set of equations for the sound pressure and acoustic particle velocity. The spatial-temporal correlation function of the scattered field is calculated. These results are obtained without using the quasi-static approximation, which is employed in the classical theory, and enable analysis of this approximation. The spatial, temporal, and frequency coherences of the scattered signal are studied. The results obtained are applied to acoustic remote sensing of the atmosphere with sodars. It is proposed that the frequency spectrum of the temporal correlation function could be used to measure the wind velocity and the variance of the convective velocity fluctuations. An ad hoc approach for increasing the spatial resolution in acoustic sounding of the atmosphere is suggested. The theory developed is rather general and applicable to acoustic pulse scattering in other media such as the ocean with temperature, salinity, and current velocity fluctuations.

Derivation of Markovian master equations for spatially correlated decoherence

We introduce a general formalism to describe the effects of Markovian noise which is spatially correlated, typically decaying over some finite correlation length. For any system of interest, this formalism describes spatial correlations without the necessity to choose a particular microscopic model for the environment. We present a method of mapping the equations to Lindblad form and discuss functional forms for homogeneous spatial correlation functions. We also discuss two example microscopic models for the environment which exhibit non-trivial spatial-temporal correlation functions.

Influence of velocity spatiotemporal correlations on the anomalous scaling exponents of passive scalars

In this paper, we consider spatial-temporal correlation functions of the turbulent velocities. With numerical simulations on the Gledzer–Ohkitani–Yamada (GOY) shell model, we show that the correlation function decays exponentially. The advecting velocity field is regarded as a colored noise field, which is spatially and temporally correlative. For comparison, we are also given the scaling exponents of passive scalars obtained by the Gaussian random velocity field, the multi-dimensional normal velocity field and the She–Leveque velocity field, introduced by She, et al. We observe that extended self-similarity scaling exponents H(p)/H(2) of passive scalar obtained by the colored noise field are more anomalous than those obtained by the other three velocity fields.

Simulation study of spatial–temporal correlation functions in supercooled liquids

We perform molecular dynamics simulations on Lennard-Jones binary mixtures of the Kob-Andersen type to investigate the properties of the dynamical heterogeneity near the glass transition. To characterize it, we focus on two types of spatial correlation functions of the direction and mobility fluctuations. Then, we predict the correlation lengths from those correlation functions. Although the correlation length obtained from the direction converges away from the glass transition point, that from the mobility fluctuation increases as the system approaches the glass transition point and has a peak near the glass transition. It suggests that the correlation of the mobility fluctuation plays an important role, more than that of the direction near the glass transition.

Study of spatial correlation functions near the glass transition by molecular dynamics simulations

We study spatial–temporal correlation functions of the direction and the mobility fluctuation by performing molecular dynamics simulations, in which the pair-interaction is described by the Lennard-Jones potential. We focus attention on coexistence states between liquid and crystal for single-component systems. Although the correlation of the direction in coexistence states is little different from that in liquids, the correlation of the mobility fluctuation in coexistence states is extremely high compared to that in liquids. In addition, we predict length scales expected from the correlation functions. The correlation lengths of both the direction and the mobility fluctuation suddenly increase at the freezing point. Especially, the length of the mobility fluctuation in coexistence states seems to diverge. We also compare the results in single-component systems to those of supercooled liquids in Lennard-Jones binary mixtures according to the suggestion that there are crystal-like ordered regions in supercooled liquids near the glass transition. Recalling the fact that the correlation lengths do not diverge even near the glass transition, its dynamics of the supercooled liquids near the glass transition and that of the coexistence states are quite different, while the static structure resembles each other.

Characterization of dynamic sea scenarios with infrared imagers

The study of marine scenes has always been a relevant subject for environmental sciences and ocean engineering. In this contribution we have analyzed infrared imagery applied to surveillance of the sea surface. We present a method based on the principal component analysis to study infrared sea scenes separating the actual scene from spatial-temporal artifacts coming from the imagers. Besides the filtering capabilities, the method obtains spatial-temporal correlation functions and the power spectrum density of the original data set. A time scale associated with the noise of the imager is defined. Solar glints identification is also addressed. One relevant feature of this method is its automatic implementation.

Fluctuations and correlations in two-dimensional Bak$ndash$Sneppen model

The self-organized criticality in the two-dimensional Bak–Sneppen model is studied from the fluctuations of the mean fitness and the jump of the minimum sites. An ensemble having the same number of updates from the initial state is used in the investigation. From the Gaussian distribution of the mean fitness in the ensemble, the lattice size dependence of the ensemble-averaged fitness is found. From the dependence, a solution to the gap equation is found and the critical gap and an exponent are calculated. A spatial–temporal correlation function is investigated from the jump of the minimum site.

Adaptive optics for airborne platforms—Part 1: modeling

Adaptive optics systems mitigate the atmospheric turbulence-induced distortion of a propagating light wavefront. The use of adaptive optics entails the design of a feedback controller, which requires the development of a model of the plant to be controlled. In adaptive optics, the plant consists of the atmosphere through which light is traveling. Moreover, a distinct feature of the adaptive optics control application is the presence of random signals in the plant. In optics, Zernike orthonormal polynomials are commonly used as a basis set for the expansion of wavefront phase distortions. Due to the atmospheric turbulence-induced random nature of the underlying physical process, the spatial-temporal correlation functions of the Zernike polynomial phase distortion expansion coefficients must be evaluated if a proper stochastic model of the plant is to be developed and adaptive optics is to be employed. In Part 1 of this paper, these correlation functions are developed using a layered atmospheric model and calculations for the first few low-order Zernike modes are performed. Using these correlation functions, an underlying stochastic linear dynamical system, which is adequate for control design, is synthesized. This system models the plant and, in turn, provides the basis for the employment of advanced model-based control and estimation concepts in an adaptive optics system for an airborne platform application.

Thermal fluctuations of electric field and solute density in biological cells

Thermal fluctuations of ionic densities in a biological cell's electrolyte creates random electric fields and solute density fluctuations. Using two common models of cellular components, the capacitor-resistor membrane model and the uniform electrolyte cytoplasm model, we determine the RMS values of these random variables and their frequency and wave number spectra by including independent variations of both anion and cation densities. In the membrane, the inequality of ionic mobilities skews the frequency spectra to much lower frequencies characteristic of solute transport, rather than current transport, through the membrane. In the cytoplasm electrolyte, the electric field wave number spectrum declines approximately exponentially with increasing wave number, leading to an algebraically declining spatial correlation function; the time correlation function also declines algebraically. The cytoplasm solute density fluctuations behave normally, with exponential spatial and algebraic temporal correlation functions. The RMS electric field of the cytoplasm is estimated at $\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}{10}^{7}$ V/m, about a factor of ${10}^{3}$ higher than that of the membrane.

Remote sensing of rainfall parameters by laser scintillation correlation method-complete equation and numerical simulation

Remote sensing of rainfall parameters by using laser scintillation effect, orginally proposed by Wang et al. is a unique approach for getting rainfall rate and raindrop size distribution with excellent temporal and spatial representativeness. In this paper, we review Wang’s work, point out the weakness of their basic equations, then establish a complete remote sensing equation in which the observable quantity, the scintillation of light intensity is used. The relationships between the rainfall parameters and the spatial-temporal correlation function of light scintillation are systematically discussed. Numerical investigations show that this equation gives at least four different ways to obtain the rainfall rate, and the kernel functions for raindrop size distribution are of excellent resolution. At last, the retrieval scheme of the drop size distribution is discussed.

Photon statistics in parametric interaction of three waves

The parametric approximation is used in a statistical analysis of the frequency conversion of an optical field by a noncentrosymmetric crystal which couples an input wave of frequency 0 < ω < ωL/2 to output waves of frequency ω+nωL(n = 0, ±1, ±2, ...; ωL is the pump frequency). An expression is obtained for the characteristic function of the output field which is described in terms of a matrix of the coupling coefficients in the case of Gaussian (displaced) statistics of the input field with independent modes. The mutual statistics of the output waves with n ≥ 0 and n' < 0 is not Gaussian but corresponds, in the lowest approximation with respect to the pump wave and in the absence of the input field, to a spontaneous (direct or cascade) decay of pump photons into photon pairs. The intensity of the radiation represented by the n ≥ 0 modes is equal to the intensity of the radiation emerging from a classical converter which receives one photon in each mode with n' < 0. The special case of three interacting modes with n = −1, 0, 1 (upconverter or light modulator) is considered in detail. The noise intensities and correlations between the numbers of photons in two and three modes are found for this case, and the spatial-temporal correlation function of the fields of the Stokes (n' = −1) and anti-Stokes (n = 1) frequencies is determined.