Third-order Correlation Functions Research Articles

The decoherence effect of qubit in 1D transverse Ising model

With the development of lab technology, the low-order correlation function can no longer describe the main effect of decoherence in the quantum many-body system, so it is imperative to study the higher-order correlation function of the system. In this paper, the higher-order correlation function is discussed analytically in the 1D transverse Ising model, and it is searched when the third-order or higher correlation functions play a key role in the decoherence effect. Under the cases of strong coupling and long coherence time, it is indicated that the effect of high-order correlation functions cannot be ignored, and the approximation of the classical Markov process is limited. But the low-order correlation function can describe well in the case of weak coupling and short coherence time.

Exotic supersolid phase of one-dimensional Bose-Hubbard model inside an optical cavity

Using a state-of-the-art numerical method density-matrix renormalization-group, we study the ground states of one-dimensional spinless Bose-Hubbard model inside a red-detuned cavity. By calculating the superfluid order, density distribution, second and third-order correlation functions, we find that there exist two novel supersolid phases with diagonal, off-diagonal orders beyond mean-field theory. One has package type density modulation along the lattice axis, another exhibits uniform density distribution. Moreover, by calculating the superradiant order parameter and the number of photon inside the cavity, we find that the novel supersolid phases are highly related to cavity-field fluctuation. Our work gives the physics beyond the mean-field theory of the Bose-Hubbard model inside an optical cavity, and provides the complete approach to fully explore the collective state of light and matter inside an optical cavity.

A Triple Correlator of Radiation Intensities of a Multimode Semiconductor Laser

In this work, temporal correlations of radiation intensities of a multimode Fabry-Perot (FP) semiconductor laser are studied. Second- and third-order intensity correlation functions are measured both for the multimode FP laser and a pulsed Ti: Sapphire (TiSp) laser. Triple correlators of the latter demonstrate an ordinary product of double correlators (the classic case). The behavior of the multimode laser is more complex and can indicate the quantum nature of optical field correlations. We follow a specific phenomenological formula for calculation of the triple temporal correlator.

Third-Order Correlation Functions for a Coulomb Pair

Third-order correlation functions for two particles with the electrostatic interaction have been obtained for the first time using the direct algebraic method. The main relations for the correlation functions that do not depend on the explicit form of the interaction potential between particles, as well as the relations that appear for four specific forms of the interaction operator, are considered.

ВІДТВОРЕННЯ СИГНАЛІВ ТА ЗОБРАЖЕНЬ ЗА БІСПЕКТРОМ У ПРИСУТНОСТІ ШУМІВ

In a number of practical applications of digital signal processing, the process under study may include correlated spectral components or phase coupling. Extracting the phase relationships provides very important and useful information for the correct understanding, analysis, and description of the properties of physical phenomena generating these processes. However, such information is irretrievably lost when using classical methods of signal processing using energy statistics, i.e. second-order statistics. Obtaining estimates of signal parameters and analyzing them using third-order correlation functions and bispectrum makes it possible to learn much more about signal properties than when using conventional correlation functions. Estimating the bispectral density (third order spectral density), in contrast to estimating the energy spectrum, makes it possible not only to describe the characteristics of the observed process correctly, but also to preserve and, if necessary, extract the phase characteristics of the component, which includes the observed process. Therefore, in a number of applied tasks of telecommunications, as well as tasks of image processing and other bisection analysis, often serves as an effective tool of signal processing. The aim of the article is to study the feasibility of using a recursive algorithm when restoring a waveform and image by bispectrum in the noise environment. The following types of signals were selected for the study: rectangular, triangular, Gaussian impulses and signal-triplet. They were distorted with additive white Gaussian noise Test image was distorted by additive white Gaussian, pulsed, Poisson and multiplicative noises. Analysis of the signal recovery results indicates that as the noise power increases, the quality of the recovery decreases. The effect of random signal shift does not affect the shape of the recovered signal. Analysis of the image recovery results indicates image recovery, but this algorithm introduces distortions in the form of an offset

Higher-order correlation functions in disordered media: Computational algorithms and application to two-phase heterogeneous materials

Macroscopic properties of heterogeneous materials, including thermal and electrical conductivity, elastic moduli, and fluid permeability, depend crucially on their microstructure. Optimal design of such materials with desired properties, as well as characterization of their microstructure, are fundamental problems that have been studied for a long time. Accurate characterization of the microstructure is possible if several $n$-point correlation functions that describe their statistical properties can be computed. While the limits $n=1$, corresponding to phase fractions, and $n=2$, that represents such two-point correlation functions as the radial distribution function, have yielded useful information and insights and have been utilized for reconstruction of models of heterogeneous materials, in many cases higher-order correlation functions are required in order to develop deeper understanding of materials' properties, as well as obtaining accurate estimates for them. We describe an algorithm for computing third-order correlation functions. We test the accuracy of the algorithm for a model of fully penetrable disks, i.e., the so-called cherry-pit model in the limit of the penetrability parameter $\ensuremath{\lambda}=0$, for which an exact expression for the three-point probability function ${S}_{3}({\mathbf{x}}_{1},{\mathbf{x}}_{2},{\mathbf{x}}_{3})$ is known. Excellent agreement between the computed results and the theoretical predictions is demonstrated. We then report on the results of extensive computations for several types of heterogeneous materials and the analysis of their three-point correlation functions. They include the probability and cluster functions ${S}_{3}$ and ${C}_{3}$, as well as the three-point surface and surface-surface-void correlation functions ${F}_{sss}$ and ${F}_{ssv}$, for a variety of two- and three-dimensional disordered materials and media.

Spontaneous Beliaev-Landau scattering out of equilibrium

We investigate Beliaev-Landau scattering in a gas of interacting photons in a coherently driven array of nonlinear dissipative resonators, as described by the 1D driven-dissipative Bose-Hubbard model. Due to the absence of detailed balance in such an out-of-equilibrium setup, steady-state properties can be much more sensitive to the underlying microscopic dynamics. As the popular truncated Wigner approximation dramatically fails in capturing this physics, we present an alternative approach, based on a systematic expansion beyond the Bogoliubov approximation, which includes the third-order correlation functions in the dynamics. As experimentally accessible signatures of Beliaev-Landau processes, we report a small but nonnegligible correction to the Bogoliubov prediction for the steady-state momentum distribution showing a characteristic series of peaks and dips, as well as non-Gaussian features in the statistics of the cavity output field.

Von Kármán-Howarth equation for three-dimensional two-fluid plasmas.

We derive the von Kármán-Howarth equation for a full three-dimensional incompressible two-fluid plasma. In the long-time limit and for very large Reynolds numbers we obtain the equivalent of the hydrodynamic "four-fifths" law. This exact law predicts the scaling of the third-order two-point correlation functions, and puts a strong constraint on the plasma turbulent dynamics. Finally, we derive a simple expression for the 4/5 law in terms of third-order structure functions, which is appropriate for comparison with in situ measurements in the solar wind at different spatial ranges.

Ultrabroadband direct detection of nonclassical photon statistics at telecom wavelength

Broadband light sources play essential roles in diverse fields, such as high-capacity optical communications, optical coherence tomography, optical spectroscopy, and spectrograph calibration. Although a nonclassical state from spontaneous parametric down-conversion may serve as a quantum counterpart, its detection and characterization have been a challenging task. Here we demonstrate the direct detection of photon numbers of an ultrabroadband (110 nm FWHM) squeezed state in the telecom band centred at 1535 nm wavelength, using a superconducting transition-edge sensor. The observed photon-number distributions violate Klyshko's criterion for the nonclassicality. From the observed photon-number distribution, we evaluate the second- and third-order correlation functions, and characterize a multimode structure, which implies that several tens of orthonormal modes of squeezing exist in the single optical pulse. Our results and techniques open up a new possibility to generate and characterize frequency-multiplexed nonclassical light sources for quantum info-communications technology.

Application of Millionschikov's hypothesis to homogeneous and isotropic turbulence possessing helicity

In this manuscript we construct a deductive theory for the stationary homogeneous turbulence, which is invariant under translations and rotations but lacks reflexional symmetry, considering the appropriate forms for the second- and third-order correlation functions. Appropriate invariant forms are considered for some second and third order correlation tensors, formed from the fluctuating components of velocity, acceleration, components of external force and pressures. In the light of the formulation of Millionschikov’s hypothesis we would point out further the treatment of first author [4] on the final period decay of isotropic turbulence using the points-merging technique employed here. We include also some enlightments of the process of future work that could be undertaken in this field of research.

Enhanced photon correlations due to strong laser-atom-cavity coupling

We investigate the resonant quantum dynamics of a laser-pumped real or artificial two-level single-atom system embedded in a leaking microcavity. We found that for stronger laser-atom-cavity couplings the generated microcavity photons exhibit larger steady-state correlations. In particular, the second- and third-order photon correlation functions are greater than the corresponding ones obtained for an incoherent light source, respectively. Furthermore, the emitted microcavity photon flux is enhanced in comparison to weaker coupling cases.

Relating statistics to dynamics in axisymmetric homogeneous turbulence

The structure and the dynamics of homogeneous turbulence are modified by the presence of body forces such that the Coriolis or the buoyancy forces, which may render a wide range of turbulence scales anisotropic. The corresponding statistical characterization of such effects is done in physical space using structure functions, as well as in spectral space with spectra of two-point correlations, providing two complementary viewpoints. In this framework, second-order and third-order structure functions are put in parallel with spectra of two-point second- and third-order velocity correlation functions, using passage relations. Such relations apply in the isotropic case, or for isotropically averaged statistics, which, however, do not reflect the actual more complex structure of anisotropic turbulence submitted to rotation or stratification. This complexity is demonstrated in this paper by orientation-dependent energy and energy transfer spectra produced in both cases by means of a two-point statistical model for axisymmetric turbulence. We show that, to date, the anisotropic formalism used in the spectral transfer statistics is especially well-suited to analyze the refined dynamics of anisotropic homogeneous turbulence, and that it can help in the analysis of isotropically computed third-order structure function statistics often used to characterize anisotropic contexts.

High-Order Correlated Motion in Single-Molecule Human Adenylate Kinase 1

The growing body of data shows protein motion plays an important role in the catalytic processes of enzymes. Human adenylate kinase 1 (AK1) is the key enzyme in maintaining the cellular energy homeostasis. The conformational change of AK1 involves large-amplitude rearrangements of the enzyme's lid domain. Observing a single molecule can remove the ensemble average, thus allows the exploration of hidden structural heterogeneity. To observe the enzyme actions of AK1 at the single-molecule level, we developed a data-taking scheme allowing us to observe the single-molecule kinetics in long time without the limitation by photobleaching. We labeled the core domain and the rim of AK with two Alexa-532 chromophores. Due to the self quenching from photo-induced electron transfer, the conformation changes of the core domain can be accurately encoded into the fluorescent intensity traces with a spatial sensitivity <1nm. Because Mg2+ ion is known to be an affecter in the energy signaling network in cells, we first investigated the effect of Mg2+ on the catalytic kinetics of AK. By analyzing the photon traces, we found that the binding of Mg2+ ions to arginines and lysines of AK increases the structural heterogeneity, which then couples to the core domain and changes the catalytic function. We further discovered that ATP/AMP substrate binding suppresses the conformation fluctuation of AK and improves the thermal stability of the core domain. The resulting third-order correlation functions of photon traces do not have time-reversal symmetry, indicating single-molecule AK is in a nonequilibrium steady state. We employed hidden Markov model with Baysian inference to verify that the photon traces are originated from transitions among three states (open, mid, close). Substrate binding to AK causes different domains of AK to move in a sequential order and suppresses the thermally-activated random motions.

First detection of galaxy-galaxy-galaxy lensing in RCS

The weak gravitational lensing effect, small coherent distortions of galaxy images by means of a gravitational tidal field, can be used to study the relation between the matter and galaxy distribution. In this context, weak lensing has so far only been used for considering a second-order correlation function that relates the matter density and galaxy number density as a function of separation. We implement two new, third-order correlation functions that have recently been suggested in the literature, and apply them to the Red-Sequence Cluster Survey. We demonstrate that it is possible, even with already existing data, to make significant measurements of third-order lensing correlations. We develop an optimised computer code for the correlation functions. To test its reliability a set of tests are performed. The correlation functions are transformed to aperture statistics, which allow easy tests for remaining systematics in the data. In order to further verify the robustness of our measurement, the signal is shown to vanish when randomising the source ellipticities. Finally, the lensing signal is compared to crude predictions based on the halo-model. On angular scales between roughly 1 arcmin and 11 arcmin a significant third-order correlation between two lens positions and one source ellipticity is found. We discuss this correlation function as a novel tool to study the average matter environment of pairs of galaxies. Correlating two source ellipticities and one lens position yields a less significant but nevertheless detectable signal on a scale of 4 arcmin. Both signals lie roughly within the range expected by theory which supports their cosmological origin.[ABRIDGED]

Exact scaling laws and the local structure of isotropic magnetohydrodynamic turbulence

This paper examines the consistency of the exact scaling laws for isotropic magnetohydrodynamic (MHD) turbulence in numerical simulations with large magnetic Prandtl numbersPmand withPm= 1. The exact laws are used to elucidate the structure of the magnetic and velocity fields. Despite the linear scaling of certain third-order correlation functions, the situation is not analogous to the case of Kolmogorov turbulence. The magnetic field is adequately described by a model of a stripy (folded) field with direction reversals at the resistive scale. At currently available resolutions, the cascade of kinetic energy is short-circuited by the direct exchange of energy between the forcing-scale motions and the stripy magnetic fields. This non-local interaction is the defining feature of isotropic MHD turbulence.

Binary and ternary textures containing higher-order spatial correlations

A quantitative method is presented for creating a large number of classes of binary (256) and ternary (7.62 × 10 12) textures. The binary textures are presented as black and white (contrasts −1 and 1). The ternary textures have three levels: black, white and the mean luminance gray (contrasts −1, 0 and 1). The ternary patterns in particular display a wide variety of properties, including depth cues from disparity and lighting. Given the very large number of ternary patterns, we present guidelines and analytical methods for selecting sets of textures with particular image qualities and/or nonlinear relationships between pixels. The second- and third-order correlation functions of several thousand examples were examined to reveal patterns that are functionally isotrigon with other textures and or with uniformly distributed noise patterns.

System of Recording Radiation for Analysis of Third-Order Correlation Functions

A system of recording the triple correlation of a photodetection signal for the spectral analysis of optical radiation is proposed. The results of the recording of the correlation components and of the computer calculation of the laser radiation spectral line profile are presented.

Model for the rotational contribution to quasielastic neutron scattering spectra from supercooled water.

A model is proposed for the first-, second-, and third-order rotational correlation functions that are required for the computation of the rotational intermediate scattering function for the calculation of incoherent quasielastic neutron scattering (QENS) spectra from supercooled water. The model is tested against molecular-dynamics data generated from an extended-simple-point-charge model of water and is found to be satisfactory. The model can be used as a practical method for extracting rotational relaxation parameters from QENS spectra measured at large Q from supercooled bulk water or interfacial water in porous materials.

Generation of large-scale structures by strong drift turbulence

The previously existing quasilinear theory of the generation of a large-scale radial electric field by small-scale drift turbulence in a plasma is generalized for the case of strong turbulence which is usually observed in experiments. The geostrophic equation (i.e., the reduced Charney-Hasegawa-Mima equation) is used to construct a systematic theory in the two-scale direct interaction approximation. It is shown that, as in the quasilinear case, drift turbulence results in a turbulent viscosity effect and leads to the renormalization of the Poisson bracket in the Charney-Hasegawa-Mima equation. It is found that, for strong drift turbulence, the viscosity coefficient is represented as a sum of two parts, which are comparable in magnitude. As in quasilinear theory, the first part is determined by the second-order correlation functions of the turbulent field and is always negative. The second part is proportional to the third-order correlation functions, and the sign of its contribution to the turbulent viscosity coefficient depends strongly on the turbulence spectrum. The turbulent viscosity coefficient is calculated numerically for the Kolmogorov spectra, which characterize the inertial interval of the drift turbulence.

Force-velocity relation and density profiles for biased diffusion in an adsorbed monolayer

In this paper, which completes our earlier short publication [Phys. Rev. Lett. 84, 511 (2000)], we study dynamics of a hard-core tracer particle (TP) performing a biased random walk in an adsorbed monolayer, composed of mobile hard-core particles undergoing continuous exchanges with a vapor phase. In terms of an approximate approach, based on the decoupling of the third-order correlation functions, we obtain the density profiles of the monolayer particles around the TP and derive the force-velocity relation, determining the TP terminal velocity, V_{tr}, as the function of the magnitude of external bias and other system's parameters. Asymptotic forms of the monolayer particles density profiles at large separations from the TP, and behavior of V_{tr} in the limit of small external bias are found explicitly.