Arbitrary Correlation Functions Research Articles

Modeling charge transfer in the photosynthetic reaction center.

In this work, we present a model to elucidate the unidirectionality of the primary charge-separation process in the bacterial reaction centers. We have used a model of three sites/molecules with electron transfer beginning at site 1 with an option to proceed to site 2 or site 3. We used a stochastic model with arbitrary correlation functions. We get the quantum yields of electron escape via the sites 2,3 in two limiting cases that correspond to a spectral density of underdamped and overdamped Brownian oscillator. In the fast modulation limit of an overdamped regime we get the effect, which was named "fear of death," in which for strong enough sink parameters the electron has a tendency to avoid the place with greater sink. The presented model was used to provide a plausible explanation of the temperature dependence of the quantum yields of the Rhodobacter sphaeroides photosynthetic reaction center in the high-temperature regime.

General solutions for multispin two-time correlation and response functions in the Glauber–Ising chain

The kinetic Glauber-Ising spin chain is one of the very few exactly solvable models of non-equilibrium statistical mechanics. Nevertheless, existing solutions do not yield tractable expressions for two-time correlation and response functions of observables involving products of more than one or two spins. We use a new approach to solve explicitly the full hierarchy of differential equations for the correlation and response functions. From this general solution follow closed expressions for arbitrary multispin two-time correlation and response functions, for the case where the system is quenched from equilibrium at T_i > 0 to some arbitrary T >= 0. By way of application, we give the results for two and four-spin two-time correlation and response functions. From the standard mapping, these also imply new exact results for two-time particle correlation and response functions in one-dimensional diffusion limited annihilation.

Spin waves in layered conductors

The spectrum of spin waves propagating in layered conductors with a quasi-bidimensional law of charge carrier dispersion was determined for the case of an arbitrary correlation function and an external magnetic field perpendicular to the conducting layers.

Estimation of spatial coherence in shallow water waveguides

For various underwater acoustic applications such as beamforming and matched field processing, it is important to understand the spatial characteristics of shallow water acoustic fields. Oceanic and geoacoustic variabilities introduce random fluctuations into the fields, for which an important metric is the spatial coherence that is the correlation function of the field. The theory developed here is based on a perturbation approach to the modal solution of the Helmholtz equation and treats scattering from sound speed fluctuations as well as from rough interfaces. The results here extend previous work to media where fluctuations can have arbitrary correlation functions and are not necessarily horizontally isotropic or homogeneous. This allows for modeling of coherence degradation due to physically realistic mechanisms. The behavior of the coherence function with respect to various parameters is illustrated using a Pekeris waveguide with superimposed randomness. The effects of several different scattering mechanisms on the coherence will be compared and rank ordered for a range of frequencies. [Work partially supported by ONR.]

Stationary correlations for a far-from-equilibrium spin chain

A kinetic one-dimensional Ising model on a ring evolves according to a generalization of Glauber rates, such that spins at even (odd) lattice sites experience a temperature T(e) (T(o)). Detailed balance is violated so that the spin chain settles into a nonequilibrium stationary state, characterized by multiple interactions of increasing range and spin order. We derive the equations of motion for arbitrary correlation functions and solve them to obtain an exact representation of the steady state. Two nontrivial amplitudes reflect the sublattice symmetries; otherwise, correlations decay exponentially, modulo the periodicity of the ring. In the long-chain limit, they factorize into products of two-point functions, in precise analogy to the equilibrium Ising chain. The exact solution confirms the expectation, based on simulations and renormalization group arguments, that the long-time, long-distance behavior of this two-temperature model is Ising-like, in spite of the apparent complexity of the stationary distribution.

Theory of open quantum systems

A quantum dissipation theory is constructed with the system–bath interaction being treated rigorously at the second-order cumulant level for both reduced dynamics and initial canonical boundary condition. The theory is valid for arbitrary bath correlation functions and time-dependent external driving fields, and satisfies correlated detailed-balance relation at any temperatures. The general formulation assumes a particularly simple form in driven Brownian oscillator systems in which the correlated driving-dissipation effects can be accounted for exactly in terms of local-field correction. Remarks on a class of widely used phenomenological quantum master equations that neglects the bath dispersion-induced dissipation are also made in contact with the present theory.

Vicious random walkers and a discretization of Gaussian random matrix ensembles

The vicious random walker problem on a one-dimensional lattice is considered. Many walkers take simultaneous steps on the lattice and the configurations in which two of them arrive at the same site are prohibited. It is known that the probability distribution of N walkers after M steps can be written in a determinant form. Using an integration technique borrowed from the theory of random matrices, we show that arbitrary kth order correlation functions of the walkers can be expressed as quaternion determinants whose elements are compactly expressed in terms of symmetric Hahn polynomials.

Steady-State Source Flow in Heterogeneous Porous Media

The flow of fluids in heterogeneous porous media is modelled by regarding the hydraulic conductivity as a stationary random space function. The flow variables, the pressure head and velocity field are random functions as well and we are interested primarily in calculating their mean values. The latter had been intensively studied in the past for flows uniform in the average. It has been shown that the average Darcy's law, which relates the mean pressure head gradient to the mean velocity, is given by a local linear relationship. As a result, the mean head and velocity satisfy the local flow equations in a fictitious homogeneous medium of effective conductivity. However, recent analysis has shown that for nonuniform flows the effective Darcy's law is determined by a nonlocal relationship of a convolution type. Hence, the average flow equations for the mean head are expressed as a linear integro-differential operator. Due to the linearity of the problem, it is useful to derive the mean head distribution for a flow by a source of unit discharge. This distribution represents a fundamental solution of the average flow equations and is called the mean Green function G d (x). The mean head G d(x) is derived here at first order in the logconductivity variance for an arbitrary correlation function ρ(x) and for any dimensionality d of the flow. It is obtained as a product of the solution G d (0)(x) for source flow in unbounded domain of the mean conductivity K A and the correction Ψ d (x) which depends on the medium heterogeneous structure. The correction Ψ d is evaluated for a few cases of interest. Simple one-quadrature expressions of Ψ d are derived for isotropic two- and three-dimensional media. The quadratures can be calculated analytically after specifying ρ (x) and closed form expressions are derived for exponential and Gaussian correlations. The flow toward a source in a three-dimensional heterogeneous medium of axisymmetric anisotropy is studied in detail by deriving Ψ3 as function of the distance from the source x and of the azimuthal angle θ. Its dependence on x, on the particular ρ(x) and on the anisotropy ratio is illustrated in the plane of isotropy (θ=0) and along the anisotropy axis (θ = π/2). The head factor k * is defined as a ratio of the head in the homogeneous medium to the mean head, k *=G d (0)/G d=Ψ d −1. It is shown that for isotropic conductivity and for any dimensionality of the flow the medium behaves as a one-dimensional and as an effective one close and far from the source, respectively, that is, lim x→0 k *(x) = K H/K A and lim x→∞ k *(x) = K efu/K A, where K A and K H are the arithmetic and harmonic conductivity means and K efu is the effective conductivity for uniform flow. For axisymmetric heterogeneity the far-distance limit depends on the direction. Thus, in the coordinate system of ρ(x) principal directions the limit values of k * are obtained as $$\begin{gathered} \tilde H_{{\text{cont}}}^ * (\mathcal{A},\mathcal{A}) = H(K_{\text{h}}^{{\text{efu}}} ) \subset _{{\text{diff}}}^ * (\mathcal{A},\mathcal{A}) = \mathcal{V}^ * ,{\text{ where }}\mathcal{A}\mathcal{U}\mathcal{R}q(\mathfrak{g})\mathfrak{k}\mathcal{U}_q (gl(2N + 1))\mathcal{R}\mathcal{B}(N) \subset \mathcal{U}_q \mathcal{F} \hfill \\ (K_{\text{h}}^{{\text{efu}}} K_{\text{v}}^{{\text{efu}}} )^{1/2} /K_{\text{A}} {\text{ for }}\theta = 0{\text{ and }}K_{\text{h}}^{{\text{efu}}} /K_{\text{A}} {\text{for }}\theta = \pi /2 \hfill \\ \end{gathered} $$ . These values differ from the corresponding components $$K_{\text{h}}^{{\text{efu}}} /K_{\text{A}} {\text{ and }}K_{\text{v}}^{{\text{efu}}} /K_{\text{A}} $$ of the effective conductivities tensor for uniform flow for θ = 0 and π/2, respectively. The results of the study are applied to solving the problem of the dipole well flow. The dependence of the mean head drop between the injection and production chambers on the anisotropy of the conductivity and the distance between the chambers is analyzed.

Quantized skyrmion fields in 2+1 dimensions

A fully quantized field theory is developped for the skyrmion topological excitations of the O(3) symmetric CP$^1$-Nonlinear Sigma Model in 2+1D. The method allows for the obtainment of arbitrary correlation functions of quantum skyrmion fields. The two-point function is evaluated in three different situations: a) the pure theory; b) the case when it is coupled to fermions which are otherwise non-interacting and c) the case when an electromagnetic interaction among the fermions is introduced. The quantum skyrmion mass is explicitly obtained in each case from the large distance behavior of the two-point function and the skyrmion statistics is inferred from an analysis of the phase of this function. The ratio between the quantum and classical skyrmion masses is obtained, confirming the tendency, observed in semiclassical calculations, that quantum effects will decrease the skyrmion mass. A brief discussion of asymptotic skyrmion states, based on the short distance behavior of the two-point function, is also presented.

Letter FFT Based Generation of Bandlimited Gaussian Noise Variates

AbstractRapid generation of time series samples of stationary, zero‐mean, correlated Gaussian noise will accelerate digital communication system simulations. In this letter, we show that a fast Fourier transform (FFT) based method is well suited to rapidly generate such noise samples. The FFT method requires O(N) memory elements and O(Nlog2 N) floating‐point operations to generate each sequence of N variates. Sequences that are bandlimited incur an aliasing error in the correlation function of the sequence, but for practical simulations we show this error is negligible. We quantify this error for arbitrary sampling rates and correlation functions.

Transport equation and diffusion in ultrathin channels and films

A rigorous perturbative transport equation for ballistic particles in thin films with random rough walls is derived by the diagrammatic Keldysh technique for both quasiclassical and quantized motion across the film. The derivation is based on canonical Migdal transformation that replaces a transport problem with random rough walls by an equivalent problem with flat boundaries and randomly distorted bulk. The rigorous derivation requires a modification of our previously used transformation to avoid non-Hermitian perturbations. The unusual nondiagonal structure of the effective scattering operator makes the transport equation different from the standard Waldmann-Snider equation when the distance between quantized levels for the motion across the film is comparable to the wall-induced perturbation. Outside of this anomalous quantum resonance region, the transport equation is similar to that for scattering by bulk impurities. The magnitude of the anomaly is calculated for degenerate particles and Gaussian correlations of surface inhomogeneities. The transport problem is solved analytically for the single-band occupancy and in the limiting cases of very large and very small correlation radii of inhomogeneities for an arbitrary correlation function of surface roughness. Elsewhere, the transport equation is analyzed numerically for the Gaussian correlation function. Transport coefficients are expressed explicitly via the angular harmonics of the surface correlation function; in the anomalous region, the results contain certain supplemental correlators. The results reveal various effects of interwall correlations on transport including an oscillatory dependence on the number of occupied minibands. The transition from quantum to quasiclassical description of ballistic motion across the (thick) film can be hindered by residual interwall interference effects similar to those in classical optic problems for thick films without bulk attenuation. Erroneous matrix elements in our previous calculations have been corrected.

Dynamical correlation functions of one-dimensional superconductors and Peierls and Mott insulators

I construct the spectral function of the Luther-Emery model which describes one-dimensional fermions with one gapless and one gapped degree of freedom, i.e. superconductors and Peierls and Mott insulators, by using symmetries, relations to other models, and known limits. Depending on the relative magnitudes of the charge and spin velocities, and on whether a charge or a spin gap is present, I find spectral functions differing in the number of singularities and presence or absence of anomalous dimensions of fermion operators. I find, for a Peierls system, one singularity with anomalous dimension and one finite maximum; for a superconductor two singularities with anomalous dimensions; and for a Mott insulator one or two singularities without anomalous dimension. In addition, there are strong shadow bands. I generalize the construction to arbitrary dynamical multi-particle correlation functions. The main aspects of this work are in agreement with numerical and Bethe Ansatz calculations by others. I also discuss the application to photoemission experiments on 1D Mott insulators and on the normal state of 1D Peierls systems, and propose the Luther-Emery model as the generic description of 1D charge density wave systems with important electronic correlations.

Stochastic wave-function approach to the calculation of multitime correlation functions of open quantum systems

Within the framework of probability distributions on projective Hilbert space a scheme for the calculation of multitime correlation functions is developed. The starting point is the Markovian stochastic wave function description of an open quantum system coupled to an environment consisting of an ensemble of harmonic oscillators in arbitrary pure or mixed states. It is shown that matrix elements of reduced Heisenberg picture operators and general time-ordered correlation functions can be expressed by time-symmetric expectation values of extended operators in a doubled Hilbert space. This representation allows the construction of a stochastic process in the doubled Hilbert space which enables the determination of arbitrary matrix elements and correlation functions. The numerical efficiency of the resulting stochastic simulation algorithm is investigated and compared with an alternative Monte Carlo wave function method proposed first by Dalibard et al. [Phys. Rev. Lett. {\bf 68}, 580 (1992)]. By means of a standard example the suggested algorithm is shown to be more efficient numerically and to converge faster. Finally, some specific examples from quantum optics are presented in order to illustrate the proposed method, such as the coupling of a system to a vacuum, a squeezed vacuum within a finite solid angle, and a thermal mixture of coherent states.

Particle Transport in the Presence of Parametric Noise

Particle transport in rod and plane geometry random media is considered. The cross section is assumed to be a continuous random function of position, with fluctuations about the mean taken as Gaussian distributed. In rod geometry, an exact closure is constructed for semi-infinite media that yields exact equations for the ensemble-averaged scalar flux Φ and current J. The same closure scheme yields a Fokker-Planck equation for the joint probability distribution function of Φ and J, from which ensemble-averaged equations for higher order quantities are derived and solved exactly for an arbitrary correlation function. Finally, the penetration of a beam of charged particles in a highly forward scattering random medium is considered, and circumstances that yield a closed ensemble-averaged transport equation are determined.

Gaussian-approximation formalism for evaluating decay of NMR spin echoes.

We present a formalism for evaluating the amplitude of the NMR spin echo and stimulated echo as a function of pulse spacings, for situations in which the nuclear spins experience an effective longitudinal magnetic field {ital h}{sub {ital z}}({ital t}) resulting from an arbitrary number of independent sources, each characterized by its own arbitrary time correlation function. The distribution of accumulated phase angles for the ensemble of nuclear spins at the time of the echo is approximated as a Gaussian. The development of the formalism is motivated by the need to understand the transverse relaxation of {sup 89}Y in YBa{sub 2}Cu{sub 3}O{sub 7}, in which the {sup 89}Y experiences {sup 63,65}Cu dipolar fields which fluctuate due to {sup 63,65}Cu {ital T}{sub 1} processes. The formalism is applied successfully to this example, and to the case of nuclei diffusing in a spatially varying magnetic field. Then we examine a situation in which the approximation fails{emdash}the classic problem of chemical exchange in dimethylformamide, where the methyl protons experience a chemical shift which fluctuates between two discrete values. In this case the Gaussian approximation yields a monotonic decay of the echo amplitude with increasing pulse spacing, while the exact solution yields distinct {open_quote}{open_quote}beats{close_quote}{close_quote}more » in the echo height, which we confirm experimentally. In light of this final example the limits of validity of the approximation are discussed. {copyright} {ital 1996 The American Physical Society.}« less

Quantum-optical input-output relations for dispersive and lossy multilayer dielectric plates.

Using the Green-function approach to the problem of quantization of the phenomenological Maxwell theory, the propagation of quantized radiation through dispersive and absorptive multilayer dielectric plates is studied. Input-output relations are derived, with special emphasis on the determination of the quantum noise generators associated with the absorption of radiation inside the dielectric matter. The input-output relations are used to express arbitrary correlation functions of the outgoing field in terms of correlation functions of the incoming field and those of the noise generators. To illustrate the theory, photons at dielectric tunneling barriers are considered. It is shown that inclusion in the calculations of losses in the photonic band gaps may substantially change the barrier traversal times. \textcopyright{} 1996 The American Physical Society.

A dynamical model for turbulence. I. General formalism

We propose new dynamical equations to describe fully developed turbulence. We begin with the Wyld equations (WE), which are exact solutions of the NSE. The WE, and their Langevin-like representation, show that nonlinearities induce a turbulent force ft(k) and a turbulent viscosity νt(k), which are given by an infinite series of Wyld diagrams. The series for νt(k) is renormalizable, and its sum can be found using RNG methods. The result, Eq. (2a), holds for stirring forces fext with an arbitrary correlation function φ and generalizes previous RNG results, which neglected ft and were limited to power law φ∼k1−2ε. To recover Kolmogorov law, these earlier RNG-based theories were forced to introduce an ad hoc stirring force with a prescribed φ∼k−3. By contrast, we show that ∼k−3 belongs to φ̃, which is the correlation function of ft, and that in the inertial range ft≫fext. The series for φ̃ cannot be summed because of a nonrenormalizable infrared divergence (IR) with an infinite number of divergent irreducible diagrams. To overcome this difficulty, we use the well-accepted notion of local energy transfer and we derive an expression for the energy flux Π(k), Eq. (2d), as well as a dynamical equation for the energy spectrum E(k), Eq. (2b). We also construct the dynamical equations for Reynolds stress spectra (solved in papers II and III). An analogous approach is developed for the temperature field. The model contains no free parameters. Some of its predictions are Kolmogorov spectrum E(k)∼k−5/3 with Ko=5/3, in agreement with recent data; temperature spectrum in the inertial-convective region Eθ∼Ba ε̄−1/3εθk−5/3, in agreement with the data; Batchelor constant Ba=σt Ko. In addition, in papers II and III we carry out extensive comparisons with the laboratory, DNS, LES data, and phenomenological models. The model can be used to construct a subgrid model for LES calculations.

The quantum statistical properties of superposition coherent states with thermal noise

Abstract We investigate a free monochromatic electromagnetic field which is in the even or odd coherent state with thermal noise. The main tool in our analysis is the characteristic function. We establish an alystic formula for an arbitrary correlation function. We point out the non-classical oscillations of the photon-number distribution and find its generating function as well as the degree of purity of the field. We also examine the squeezing properties and antibunching feature. Besides, the usual quasiprobability densities are derived.

The quantum statistical properties of superposition coherent states with thermal noise

Abstract We investigate a free monochromatic electromagnetic field which is in the even or odd coherent state with thermal noise. The main tool in our analysis is the characteristic function. We establish an alystic formula for an arbitrary correlation function. We point out the non-classical oscillations of the photon-number distribution and find its generating function as well as the degree of purity of the field. We also examine the squeezing properties and antibunching feature. Besides, the usual quasiprobability densities are derived.

Free inertial processes driven by Gaussian noise: Probability distributions, anomalous diffusion, and fractal behavior.

We study the motion of an unbound particle under the influence of a random force modeled as Gaussian colored noise with an arbitrary correlation function. We derive exact equations for the joint and marginal probability density functions and find the associated solutions. We analyze in detail anomalous diffusion behaviors along with the fractal structure of the trajectories of the particle and explore possible connections between dynamical exponents of the variance and the fractal dimension of the trajectories.