Correlation Functions Of Fields Research Articles

Perturbative BF theory

We consider a superrenormalisable gauge theory of topological type, in which the structure group is equal to the inhomogeneous group ISU(2). The generating functional of the correlation functions of the gauge fields is derived and its connection with the generating functional of the Chern-Simons theory is discussed. The complete renormalisation of this model defined in R3 is presented. The structure of the ISU(2) conjugacy classes is determined. Gauge invariant observables are defined by means of appropriately normalised traces of ISU(2) holonomies associated with oriented, framed and coloured knots. The perturbative evaluation of the Wilson lines expectation values is investigated and the up-to-third-order contributions to the perturbative expansion of the observables, which correspond to knot invariants, are produced. The general dependence of the knot observables on the framing is worked out.

Photons statistics in a hybrid electro-optomechanical system: effect of optomechanical interaction

In this paper, an electro-optomechanical system in which a microwave cavity and an optical one are simultaneously coupled to a mechanical oscillator, is considered. There are also two applied driving fields to the cavities and finally, dissipation effects are taken into account for this system. Using the Heisenberg–Langevin method, temporal evolution of the second order correlation functions (for optical field, mechanical oscillator and their cross correlations), are evaluated. We show that how the optomechanical coupling can affect on the correlation functions of the system. In this way we will show that the presence of optomechanical interaction in the system can lead to photon blockade effect. Moreover, we show that the presence and increasing of the optomechanical coupling lead to appearing squeezed states in the mean photon number of the optical cavity.

Application of multiple scattering theory to Doppler velocimetry of ejecta from shock-loaded samples

We address the actual problem of retrieving the physical parameters of ejecta from data of heterodyne Doppler velocimetry. Under the assumption that ejected particles are randomly spaced and their number within the probed volume is great, the noise-free component of the power spectrum of heterodyne beats is shown to be expressed in terms of a solution to the transport equation for the field correlation function which accounts for multiple scattering and absorption of the probing beam in the ejecta cloud. This provides a means for theoretical modeling of experimental Doppler data. The ejecta cloud is considered as a plane layer of particles moving in the air away from the free-surface of the shock-loaded sample. The spatial profile of the scattering coefficient and the cloud thickness are related directly to the distribution of ejected particles over velocities and coordinates. The slowing-down of ejected particles in the air leads to an ambiguous relation between the velocity of particles and their position, resulting in essential complication of the particle distribution. Using a multi-group description of the ejecta cloud, we reduce the transport equation to a system of linked Milne-like equations. The system is solved numerically with the discrete ordinate code. Varying the values of the cloud optical thickness and the parameters of the particle distribution over sizes and initial velocities, we fit the calculated spectrum to the time-resolved data of heterodyne Doppler measurements. Such an approach enables retrieving the primary ejecta characteristics (the total ejected mass, the density-velocity profile and the size distribution of ejected particles) directly from heterodyne experiments. Application of the proposed method to the velocimetry data on ejecta is presented.

The Interaction Potential between an Atom and a Conductive Wall

In this work, the interaction potential between an atom (with definite Static Polarizability) and a perfect neutral conductive wall is evaluated in two approaches. First, using, the explicit form of the singlet and doublet parts of the vacuum vector potential operator in atomic quadratic stark shift formula and taking the expectation value in vacuum state. Second, writing, the quadratic stark shift formula in terms of electric field correlation function, relating the correlation function to the imaginary parts of the vector potential Green function tensor components (via fluctuation dissipation theorem in statistical mechanics) and the evaluation of the required vector potential Green function tensor components. The consistency of the two methods is shown.

Bootstrapping inflationary correlators in Mellin space

We develop a Mellin space approach to boundary correlation functions in anti-de Sitter (AdS) and de Sitter (dS) spaces. Using the Mellin-Barnes representation of correlators in Fourier space, we show that the analytic continuation between AdSd+1 and dSd+1 is encoded in a collection of simple relative phases. This allows us to determine the late-time tree-level three-point correlators of spinning fields in dSd+1 from known results for Witten diagrams in AdSd+1 by multiplication with a simple trigonometric factor. At four point level, we show that Conformal symmetry fixes exchange four-point functions both in AdSd+1 and dSd+1 in terms of the dual Conformal Partial Wave (which in Fourier space is a product of boundary three-point correlators) up to a factor which is determined by the boundary conditions. In this work we focus on late-time four-point correlators with external scalars and an exchanged field of integer spin-ℓ. The Mellin-Barnes representation makes manifest the analytic structure of boundary correlation functions, providing an analytic expression for the exchange four-point function which is valid for general d and generic scaling dimensions, in particular massive, light and (partially-)massless fields. It moreover naturally identifies boundary correlation functions for generic fields with multi-variable Meijer-G functions. When d = 3 we reproduce existing explicit results available in the literature for external conformally coupled and massless scalars. From these results, assuming the weak breaking of the de Sitter isometries, we extract the corresponding correction to the inflationary three-point function of general external scalars induced by a general spin- ℓ field at leading order in slow roll. These results provide a step towards a more systematic understanding of de Sitter observables at tree level and beyond using Mellin space methods.

Theory of two atoms in a chiral waveguide

A theory is presented that describes the atom and field dynamics for two atoms in a chiral waveguide. A source-field approach is used that enables one to identify the various physical processes contributing to these dynamics. Each atom is prepared in an arbitrary state at $t=0$ and the field intensity and correlation functions are calculated, fully accounting for retardation. When the atoms are prepared in identical superposition states, the effects of constructive and destructive interference play a significant role on both the field intensity and second-order correlation function. It is also shown that the results can be taken over to provide a solution for the related problem of a single-photon pulse incident on an atom prepared in an arbitrary initial state.

Correlators of the symmetric product orbifold

We exploit null vectors of the fractional Virasoro algebra of the symmetric product orbifold to compute correlation functions of twist fields in the large N limit. This yields a new method to derive correlation functions in these orbifold CFTs that is purely based on the symmetry algebra. We explore various generalisations, such as subleading (torus) contributions or correlation functions of other fields than the bare twist fields. We comment on the consequences of our computation for the AdS3/CFT2 correspondence.

Marked correlation functions in perturbation theory

We develop perturbation theory approaches to model the marked correlation function constructed to up-weight low density regions of the Universe, which might help distinguish modified gravity models from the standard cosmology model based on general relativity. Working within Convolution Lagrangian Perturbation Theory, we obtain that weighted correlation functions are expressible as double convolution integrals that we approximate using a combination of Eulerian and Lagrangian schemes. We find that different approaches agree within 1% on quasi non-linear scales. Compared with N-body simulations, the perturbation theory is found to provide accurate predictions for the marked correlation function of dark matter fields, dark matter halos as well as Halo Occupation Distribution galaxies down to 30 Mpc/h. These analytic approaches help to understand the degeneracy between the mark and the galaxy bias and find a way to maximize the differences among various cosmological models.

A Mellin space approach to cosmological correlators

We propose a Mellin space approach to the evaluation of late-time momentum-space correlation functions of quantum fields in (d + 1)-dimensional de Sitter space. The Mellin-Barnes representation makes manifest the analytic structure of late-time correlators and, more generally, provides a convenient general d framework for the study of conformal correlators in momentum space. In this work we focus on tree-level correlation functions of general scalars as a prototype, including n-point contact diagrams and 4-point exchanges. For generic scalars, both the contact and exchange diagrams are given by (generalised) Hypergeometric functions, which reduce to existing expressions available in the literature for d = 3 and external scalars which are either simultaneously conformally coupled or massless. This approach can also be used for the perturbative bulk evaluation of momentum space boundary correlators in (d + 1)-dimensional anti-de Sitter space (Witten diagrams).

CPT‐Based Probabilistic Characterization of Undrained Shear Strength of Clay

Applying random field theory involves two important issues: the statistical homogeneity (or stationarity) and determination of random field parameters and correlation function. However, the profiles of soil properties are typically assumed to be statistically homogeneous or stationary without rigorous statistical verification. It is also a challenging task to simultaneously determine random field parameters and the correlation function due to a limited amount of direct test data and various uncertainties (e.g., transformation uncertainties) arising during site investigation. This paper presents Bayesian approaches for probabilistic characterization of undrained shear strength using cone penetration test (CPT) data and prior information. Homogeneous soil units are first identified using CPT data and subsequently assessed for weak stationarity by the modified Bartlett test to reject the null hypothesis of stationarity. Then, Bayesian approaches are developed to determine the random field parameters and simultaneously select the most probable correlation function among a pool of candidate correlation functions within the identified statistically homogeneous layers. The proposed approaches are illustrated using CPT data at a clay site in Shanghai, China. It is shown that Bayesian approaches provide a rational tool for proper determination of random field model for probabilistic characterization of undrained shear strength with consideration of transformation uncertainty.

Denoising ambient seismic field correlation functions with convolutional autoencoders

SUMMARYSeismic interferometry is an established method for monitoring the temporal evolution of the Earth’s physical properties. We introduce a new technique to improve the precision and temporal resolution of seismic monitoring studies based on deep learning. Our method uses a convolutional denoising autoencoder, called ConvDeNoise, to denoise ambient seismic field correlation functions. The technique can be applied to traditional two-station cross-correlation functions but this study focuses on single-station cross-correlation (SC) functions. SC functions are computed by cross correlating the different components of a single seismic station and can be used to monitor the temporal evolution of the Earth’s near surface. We train and apply our algorithm to SC functions computed with a time resolution of 20 min at seismic stations in the Tokyo metropolitan area, Japan. We show that the relative seismic velocity change [dv/v(t)] computed from SC functions denoised with ConvDeNoise has less variability than that calculated from raw SC functions. Compared to other denoising methods such as the SVD-based Wiener Filter method developed by Moreau et al., the dv/v results obtained after using our algorithm have similar precision. The advantage of our technique is that once the algorithm is trained, it can be apply to denoise near-real-time SC functions. The near-real-time aspect of our denoising algorithm may be useful for operational hazard forecasting models, for example when applying seismic interferometry at an active volcano.

Toverline{T} deformation of correlation functions

We study the evolution of correlation functions of local fields in a two-dimensional quantum field theory under the lambda Toverline{T} deformation, suitably regularized. We show that this may be viewed in terms of the evolution of each field, with a Dirac-like string being attached at each infinitesimal step. The deformation then acts as a derivation on the whole operator algebra, satisfying the Leibniz rule. We derive an explicit equation which allows for the analysis of UV divergences, which may be absorbed into a non-local field renormalization to give correlation functions which are UV finite to all orders, satisfying a (deformed) operator product expansion and a Callan-Symanzik equation. We solve this in the case of a deformed CFT, showing that the Fourier-transformed renormalized two-point functions behave as k2∆+2λk2, where ∆ is their IR conformal dimension. We discuss in detail deformed Noether currents, including the energy-momentum tensor, and show that, although they also become non-local, when suitably improved they remain finite, conserved and satisfy the expected Ward identities. Finally, we discuss how the equivalence of the Toverline{T} deformation to a state-dependent coordinate transformation emerges in this picture.

On the gauge-invariant path-integral measure for the overlap Weyl fermions in 16 of SO(10)

AbstractWe consider the lattice formulation of SO(10) chiral gauge theory with left-handed Weyl fermions in the 16-dimensional spinor representation ($\underline{16}$) within the framework of the overlap fermion/Ginsparg–Wilson relation. We define a manifestly gauge-invariant path-integral measure for the left-handed Weyl field using all the components of the Dirac field, but the right-handed part of it is just saturated completely by inserting a suitable product of the SO(10)-invariant ’t Hooft vertices in terms of the right-handed field. The definition of the measure applies to all possible topological sectors of admissible link fields. The measure possesses all required transformation properties under lattice symmetries and the induced effective action is CP invariant. The global U(1) symmetry of the left-handed field is anomalous due to the non-trivial transformation of the measure, while that of the right-handed field is explicitly broken by the ’t Hooft vertices. There remains the issue of smoothness and locality in the gauge-field dependence of the Weyl fermion measure, but the question is well defined and the necessary and sufficient condition for this property is formulated in terms of the correlation functions of the right-handed auxiliary fields. In the weak gauge-coupling limit at least, all the auxiliary fields have short-range correlations and the question can be addressed further by Monte Carlo methods without encountering the sign problem. We also discuss the relations of our formulation to other approaches/proposals to decouple the species doubling/mirror degrees of freedom. These include the Eichten–Preskill model, the mirror-fermion model with overlap fermions, the domain-wall fermion model with the boundary Eichten–Preskill term, 4D topological insulator/superconductor with a gapped boundary phase, and the recent studies on the PMS phase/“mass without symmetry breaking”. We clarify the similarities and differences in the technical details and show that our proposal is a unified and well defined testing ground for that basic question.

Stochastic quasi-Gaussian models of atmospheric clouds

Random field simulation methods that can be used to simulate the stochastic structure of three-dimensional clouds are discussed. Examples of homogeneous random field realizations that reproduce one-dimensional distributions and correlation functions of experimental fields of stratus optical thicknesses are presented.

Material equations in electrodynamics of medium consisting of two-level emitters

The process of self-ordering in the famous Dicke model was studied in the framework of eliminating the boson variables. But the reduced description method enables us to obtain also the picture of electromagnetic field evolution provided field amplitudes and correlation functions are included into the number of reduced description parameters. In the Dicke Hamiltonian structure the interaction term includes the operators of emitter dipole moments or dipole moment density (polarization) since a spatial system is under consideration. Thus operator evolution equations are based on using such operators and their derivatives. The chain of evolution equations for averaged field amplitudes and binary correlation functions are obtained with using the statistical operator calculated in a perturbation theory in quasispin-photon interaction assumed to be small. The problem of chain decoupling does not arise since at any step we have a closed set of equations. The sets should be solved on the basis of material equations for current density and their generalizations for more complicated correlation functions. The way to constructing such equations and estimating the material parameters which are necessary for the numerical modeling of the development of correlations is discussed in the paper.

Generalization of the exponential basis for tensor network representations of long-range interactions in two and three dimensions

In one dimension (1D), a general decaying long-range interaction can be fit to a sum of exponential interactions $e^{-\lambda r_{ij}}$ with varying exponents $\lambda$, each of which can be represented by a simple matrix product operator (MPO) with bond dimension $D=3$. Using this technique, efficient and accurate simulations of 1D quantum systems with long-range interactions can be performed using matrix product states (MPS). However, the extension of this construction to higher dimensions is not obvious. We report how to generalize the exponential basis to 2D and 3D by defining the basis functions as the Green's functions of the discretized Helmholtz equation for different Helmholtz parameters $\lambda$, a construction which is valid for lattices of any spatial dimension. Compact tensor network representations can then be found for the discretized Green's functions, by expressing them as correlation functions of auxiliary fermionic fields with nearest neighbor interactions via Grassmann Gaussian integration. Interestingly, this analytic construction in 3D yields a $D=4$ tensor network representation of correlation functions which (asymptotically) decay as the inverse distance ($r^{-1}_{ij}$), thus generating the (screened) Coulomb potential on a cubic lattice. These techniques will be useful in tensor network simulations of realistic materials.

Frequency-, Time-, and Wavevector-Resolved Ultrafast Incoherent Diffraction of Noisy X-ray Pulses.

We study theoretically incoherent time-resolved X-ray diffraction of fluctuating sources such as free electron lasers, as well as coherent sources with controllably added randomness. We find that the temporal resolution is strongly eroded by the noise. By considering frequency resolution of the signal, we find that the statistical properties of the noise carry important information allowing us to restore the temporal resolution. We propose a multidimensional stochastic resonance treatment to shape the optical window and extract this information from signals. Using the frequency-dependent stochastic phase as a frequency marker allows to improve the spectral resolution as well via intensity correlations. Frequency-tuned field correlation functions are used to modify the effective frequency gating and extract specific charge density contributions to the diffraction pattern while maintaining temporal resolution.

Observing Mesospheric Turbulence With Specular Meteor Radars: A Novel Method for Estimating Second‐Order Statistics of Wind Velocity

There are few observational techniques for measuring the distribution of kinetic energy within the mesosphere with a wide range of spatial and temporal scales. This study describes a method for estimating the three‐dimensional mesospheric wind field correlation function from specular meteor trail echoes. Each radar echo provides a measurement of a one‐dimensional projection of the wind velocity vector at a randomly sampled point in space and time. The method relies on using pairs of such measurements to estimate the correlation function of the wind with different spatial and temporal lags. The method is demonstrated using a multistatic meteor radar data set that includes ≈105 meteor echoes observed during a 24‐hr time period. The new method is found to be in good agreement with the well‐established technique for estimating horizontal mean winds. High‐resolution correlation functions with temporal, horizontal, and vertical lags are also estimated from the data. The temporal correlation function is used to retrieve the kinetic energy spectrum, which includes the semidiurnal mode and a 3‐hr period wave. The horizontal and vertical correlation functions of the wind are then used to derive second‐order structure functions, which are found to be compatible with the Kolmogorov prediction for spectral distribution of kinetic energy in the turbulent inertial range. The presented method can be used to extend the capabilities of specular meteor radars. It is relatively flexible and has a multitude of applications beyond what has been shown in this study.

Quantum photonic transistor controlled by an atom in a Floquet cavity-QED system.

The photon transmission of a Floquet cavity quantum electrodynamic (QED) system containing three periodically modulated cavities interacting with a two-level atom is investigated. The input-output relations and the second-order correlation functions of the output fields are calculated. The system demonstrates the feature of a quantum photonic transistor, i.e., the photon transmission is controlled by the quantum states of the atom. This device can be used as a building block for various quantum information processing.

Coupling coefficient in three dimensional higher spin holography

We consider linearised Vasiliev's equations around the background AdS field in three dimensions for the scalar-scalar-higher spin field correlation function. Relating this with the higher spin field determined in the metric formulation allows determination of the corresponding coupling coefficient. The result agrees with the analogous computation for the spin three field.