Field-field Correlation Function Research Articles

Wigner distribution function approach to analyze MIMO communication within a waveguide

Multiple-input-multiple-output (MIMO) communication is a technology to create high capacity wireless links. The main aim of this paper is to provide a foundation to mathematically model wireless chip to chip communication within complex enclosures. This paper mainly concentrates on modelling wave propagation between transmit and receive antennas through a phase space approach which exploits the relationship between the field-field correlation function (CF) and the Wigner distribution function (WDF). A reliable model of wireless chip-to-chip (C2C) communication helps mitigate the information bottleneck caused due to the wired connections between chips, thus, help improve the efficiency of electronic devices of the future. Placing complex sources such as printed circuit board (PCB) inside a cavity or enclosure results in multi-path interference and hence makes the prediction of signal propagation more difficult. Thus, the CFs can be propagated based on a ray transport approach that predicts the average radiated density, but not the significant fluctuations that occur about it. Hence, the WDF approach can be extended to problems in finite cavities that incorporates reflections as well. Phase space propagators based on classical multi-reflection ray dynamics can be obtained by considering the high-frequency asymptotics.

An asymptotic formula for sound radiation from plates

We present a new approach to the modelling of sound radiated from vibrating structures that will provide a platform for simulation of larger problems by the method of Dynamical Energy Analysis (DEA), which characterises sound using densities in a ray-dynamical phase space. We consider in particular the radiated acoustic power from plates with diffuse bending vibrations, which we characterise using a two-point correlation function of normal velocities. Such field-field correlation functions are transformed to ray-dynamical phase space densities using a Wigner transformation, which allows insertion into ray-based methods such as DEA. Using correlation functions to characterise plate vibrations also allows the method to cater for stochastic, noisy driving of such systems. The results for the radiation efficiency of a plate are presented in an asymptotic form, with leading contributions from the plate interior and its boundary and with corner corrections also being given for particular boundary conditions and right-angled corners. A notable feature of this analysis is that the bulk contribution vanishes below a critical frequency, and the asymptotic estimate of radiated power then leads with a boundary contribution. This is shown to agree well with a more traditional calculation based on modal analysis in the special case of a rectangular plate.

Generalized Fluctuation-Dissipation Theorem for Non-equilibrium Spatially Extended Systems

The fluctuation-dissipation theorem (FDT) connecting the response of the system to external perturbations with the fluctuations at thermodynamic equilibrium is a central result in statistical physics. There has been effort devoted to extending the FDT in several different directions since its original formulation. In this work we establish a generalized form of the FDT for spatially extended nonequilibrium stochastic systems described by continuous fields. The generalized FDT is formulated with the aid of the nonequilibrium force decomposition in the potential landscape and flux field theoretical framework. The general results are substantiated in the setting of the Ornstein-Uhlenbeck (OU) process and further illustrated by a more specific example worked out in detail. The key feature of this generalized FDT for nonequilibrium spatially extended systems is that it represents a ternary relation rather than a binary relation as the FDT for equilibrium systems does. In addition to the response function and the time derivative of the field-field correlation function that are present in the equilibrium FDT, the field-flux correlation function also enters the generalized FDT. This additional contribution originates from detailed balance breaking that signifies the nonequilibrium irreversible nature of the steady state. In the special case when the steady state is an equilibrium state obeying detailed balance, the field-flux correlation function vanishes and the ternary relation in the generalized FDT reduces to the binary relation in the equilibrium FDT.

Babinet's principle for mutual intensity.

In classical diffraction theory, Babinet's principle relates the electromagnetic fields produced by complementary sources. This theorem was always formulated for single-point quantities, both intensities or field amplitudes, in conditions where the full spatial coherence is implicitly assumed. However, electromagnetic fields are, in general, partially coherent, and their spatial properties are described in terms of two-point field-field correlation functions. In this case, a generalized Babinet's principle can be derived that applies to the spatial coherence functions. We present both the derivation and the experimental demonstration of this generalized Babinet theorem.

Fermi's golden rule forN-body systems in a blackbody radiation

We review the calculation of Fermi's golden rule for a system of $N$-body dipoles, magnetic or electric, weakly interacting with a blackbody radiation. By using the magnetic or electric field-field correlation function evaluated in the 1960s for the black body radiation, we deduce a general formula for the transition rates and study its limiting, fully coherent or fully incoherent, regimes.

Correlation lengths of the repulsive one-dimensional Bose gas

We investigate the large-distance asymptotic behavior of the static density-density and field-field correlation functions in the one-dimensional Bose gas at finite temperature. The asymptotic expansions of the Bose gas correlators are obtained performing a specific continuum limit in the similar low-temperature expansions of the longitudinal and transversal correlation functions of the $XXZ$ spin chain. In the lattice system the correlation lengths are computed as ratios of the largest and next-largest eigenvalues of the $XXZ$ spin chain quantum transfer matrix. In both cases, lattice and continuum, the correlation lengths are expressed in terms of solutions of Yang-Yang type [C. N. Yang and C. P. Yang, J. Math. Phys. 10, 1151 (1969)] nonlinear integral equations which are easily implementable numerically.

Dynamic heterodyne near field scattering

The technique heterodyne near field scattering (HNFS), originally developed for low-angle static light scattering, has also been implemented for carrying out dynamic light scattering. While the classical dynamic light scattering method measures the intensity-intensity correlation function, dynamic HNFS gives directly the field-field correlation function, without any assumption on the statistical properties of the sample, as the ones required by the Siegert relation. The technique has been tested with calibrated Brownian particles and its performances compared to those of the classical dynamic light scattering method.

Fluctuations in diffuse field–field correlations and the emergence of the Green’s function in open systems

Recent intense interest in diffuse field correlation functions, with applications to passive imaging in underwater acoustics and seismology, has raised questions about the degree with which a retrieved waveform can be expected to conform to the Green's function, and in particular the degree with which a ray arrival may be discerned. On considering a simple scalar wave model consisting of fields with distributed random sources, the difffuse field-field correlation function R is defined as a sum of correlation integrals, one for each of the many distinct distributed sources. It is then shown that this ensemble of fields has a correlation function with expectation (R) equal to the Green's function. This model also lends itself to calculations of the variance of R, and thus to estimates of the degree to which an R calculated using finite amounts of data will conform to the Green's function. The model predicts that such conformation is strongest at low frequencies. Ray arrivals are detectable if sufficient data have been collected, but the amount of data needed scales in three dimensions with the square of the source-receiver separation, and the square of the frequency. Applications to seismology are discussed.

Statistical mechanics of double sinh-Gordon kinks

We study the classical thermodynamics of the double sinh-Gordon (DSHG) theory in 1 + 1 dimensions. This model theory has a double well potential V( φ) = ( ζ cosh2 φ− n) 2 when n > ζ, thus allowing for the existence of kinks and antikinks. Though it is non-integrable, the DSHG model is remarkably amenable to analysis. Below we obtain exact single kink and kink lattice solutions as well as the asymptotic kink-antikink interaction. In the continuum limit, finding the classical partition function is equivalent to solving for the ground state of a Schrödinger-like equation obtained via the transfer integral method. For the DSHG model, this equation turns out to be quasi-exactly solvable. We exploit this property to obtain exact energy eigenvalues and wavefunctions for several temperatures both above and below the symmetry breaking transition temperature (provided n = 1, 2, …, 6). The availability of exact results provides an excellent testing ground for large scale Langevin simulations. The probability distribution function (PDF) calculated from Langevin dynamics is found to be in striking agreement with the exact PDF obtained from the ground state wavefunction. This validation points to the utility of a PDF-based computation of thermodynamics utilizing Langevin methods. In addition to the PDF, field-field and field fluctuation correlation functions were computed and also found to be in excellent agreement with the exact results.

Frequency-fluctuation model for line-shape calculations in plasma spectroscopy.

A model is developed that permits the calculation of the radiation emitted by complex or highly charged ions in a plasma. The model is based on the usual separation of the plasma-emitter interaction into the homogeneous broadening effects of the fast electrons and the inhomogeneous broadening arising from slow ions. For plasma conditions where the ion motion can be neglected, the spectrum is the usual static line shape. To account for ion dynamics, the frequency-fluctuation model is introduced by decomposing the line shape of each radiative transition into a sum of radiative channels that are associated with the smallest observable inhomogeneities that form the static profile. The fluctuations of the ion microfield, the ion dynamics effect, is modeled by an exchange process between the static radiative channels. This results in both a smoothing and an overall coalescence of the radiative channels and depends strongly on an averaged characteristic fluctuation rate associated with the dynamics of the interaction of the local plasma microfield with the ion. This rate is formally related to the double-time field-field correlation function behavior. This stochastic model of the observed frequency fluctuations permits fast and accurate calculations of the emitted spectral profiles, including ion dynamics emitted by complex ions in a wide range of plasma conditions.

Asymptotics of a time correlation function in multiple recurrent scattering of scalar waves

We consider an integral that recently showed up in the calculation of the time-dependent field-field correlation function of the electric field inside polarizable (dielectric) particles. We derive new integral representations on which numerical algorithms can be based and which give information on the asymptotic behaviour for large values of a time parameter. We interpret the results of the paper in terms of the physical problem.

Correlation functions of the one-dimensional Hubbard model in a magnetic field.

We present a general method for the calculation of correlation functions in the repulsive one-dimensional Hubbard model at less than half-filling in a magnetic field h. We describe the dependence of the critical exponents that drive their long-distance asymptotics on the Coulomb coupling, the density, and h. This dependence can be described in terms of a set of coupled Bethe-Ansatz integral equations. It simplifies significantly in the strong-coupling limit, where we give explicit formulas for the dependence of the critical exponents on the magnetic field. In particular, we find that at small field the functional dependence of the critical exponents on h can be algebraic or logarithmic---depending on the operators involved. In addition, we evaluate the singularities of the Fourier images of the correlation functions. It turns out that switching on a magnetic field gives rise to singularities in the dynamic field-field correlation functions that are absent at h=0.

Classical and Nonclassical Optical Diffusion

ABSTRACTWe present a brief summary of our recent work on classical and nonclassical optical diffusion in disorder metal oxides. Results on the optical transmission through a slab of titania spheres is presented and discussed in some detail illustrating the experimental method for obtaining the optical diffusion coefficient and photon absorption time from the transmission data. We conclude that the optical field-field correlation function with frequency is the Fourier transform of the time of flight distribution.