Showing papers on "Correlation function (statistical mechanics) published in 2012"

Multi-frame pyramid correlation for time-resolved PIV

Abstract: A novel technique is introduced to increase the precision and robustness of time-resolved particle image velocimetry (TR-PIV) measurements. The innovative element of the technique is the linear combination of the correlation signal computed at different separation time intervals. The domain of the correlation signal resulting from different temporal separations is matched via homothetic transformation prior to the averaging of the correlation maps. The resulting ensemble-averaged correlation function features a significantly higher signal-to-noise ratio and a more precise velocity estimation due to the evaluation of a larger particle image displacement. The method relies on a local optimization of the observation time between snapshots taking into account the local out-ofplane motion, continuum deformation due to in-plane velocity gradient and acceleration errors. The performance of the pyramid correlation algorithm is assessed on a synthetically generated image sequence reproducing a three-dimensional Batchelor vortex; experiments conducted in air and water flows are used to assess the performance on time-resolved PIV image sequences. The numerical assessment demonstrates the effectiveness of the pyramid correlation technique in reducing both random and bias errors by a factor 3 and one order of magnitude, respectively. The experimental assessment yields a significant increase of signal strength indicating enhanced measurement robustness. Moreover, the amplitude of noisy fluctuations is considerably attenuated and higher precision is obtained for the evaluation of time-resolved velocity and acceleration.

Exact time evolution of space- and time-dependent correlation functions after an interaction quench in the one-dimensional Bose gas

Abstract: We consider the non-equilibrium dynamics of the interacting Lieb–Liniger gas after instantaneously switching the interactions off. The subsequent time evolution of the space- and time-dependent correlation functions is computed exactly. Different relaxation behavior is observed for different correlation functions. The long time average is compared with the predictions of several statistical ensembles. The generalized Gibbs ensemble restricted to a fixed number of particles is shown to give correct results at large times for all length scales.

Imaging a full set of optical scattering properties of biological tissue by inverse spectroscopic optical coherence tomography

Abstract: We here develop a method to measure and image the full optical scattering properties by inverse spectroscopic optical coherence tomography (ISOCT). Tissue is modelled as a medium with continuous refractive index (RI) fluctuation and such a fluctuation is described by the RI correlation functions. Under the first-order Born approximation, the forward model is established for ISOCT. By measuring optical quantities of tissue including the scattering power of the OCT spectrum, the reflection albedo α defined as the ratio of scattering coefficient μ(s), and the backscattering coefficient μ(b), we are able to inversely deduce the RI correlation function and image the full set of optical scattering properties.

Wave functions and correlation functions for GKP strings from integrability

Abstract: We develop a general method of computing the contribution of the vertex operators to the semi-classical correlation functions of heavy string states, based on the state-operator correspondence and the integrable structure of the system. Our method requires only the knowledge of the local behavior of the saddle point configuration around each vertex insertion point and can be applied to cases where the precise forms of the vertex operators are not known. As an important application, we compute the contributions of the vertex operators to the three-point functions of the large spin limit of the Gubser-Klebanov-Polyakov (GKP) strings in AdS 3 spacetime, left unevaluated in our previous work [ arXiv:1110.3949 ] which initiated such a study. Combining with the finite part of the action already computed previously and with the newly evaluated divergent part of the action, we obtain finite three-point functions with the expected dependence of the target space boundary coordinates on the dilatation charge and the spin.

Multiple length and time scales of dynamic heterogeneities in model glass-forming liquids: A systematic analysis of multi-point and multi-time correlations

Abstract: We report an extensive and systematic investigation of the multi-point and multi-time correlation functions to reveal the spatio-temporal structures of dynamic heterogeneities in glass-forming liquids. Molecular dynamics simulations are carried out for the supercooled states of various prototype models of glass-forming liquids such as binary Kob-Andersen, Wahnstrom, soft-sphere, and network-forming liquids. First, we quantify the length scale of the dynamic heterogeneities utilizing the four-point correlation function. The growth of the dynamic length scale with decreasing temperature is characterized by various scaling relations that are analogous to the critical phenomena. We also examine how the growth of the length scale depends upon the model employed. Second, the four-point correlation function is extended to a three-time correlation function to characterize the temporal structures of the dynamic heterogeneities based on our previous studies. We provide comprehensive numerical results obtained from the three-time correlation function for the above models. From these calculations, we examine the time scale of the dynamic heterogeneities and determine the associated lifetime in a consistent and systematic way. Our results indicate that the lifetime of the dynamical heterogeneities becomes much longer than the alpha relaxation time determined from a two-point correlation function in fragile liquids. The decoupling between the two time scales is remarkable, particularly in supercooled states, and the time scales differ by more than an order of magnitude in a more fragile liquid. In contrast, the lifetime is shorter than the alpha-relaxation time in tetrahedral network-forming strong liquid, even at lower temperatures.

Mode-coupling theory of the glass transition for confined fluids.

Abstract: We present a detailed derivation of a microscopic theory for the glass transition of a liquid enclosed between two parallel walls relying on a mode-coupling approximation. This geometry lacks translational invariance perpendicular to the walls, which implies that the density profile and the density-density correlation function depends explicitly on the distances to the walls. We discuss the residual symmetry properties in slab geometry and introduce a symmetry adapted complete set of two-point correlation functions. Since the currents naturally split into components parallel and perpendicular to the walls the mathematical structure of the theory differs from the established mode-coupling equations in bulk. We prove that the equations for the nonergodicity parameters still display a covariance property similar to bulk liquids.

Heterogeneous and anisotropic dynamics of a 2D gel.

Abstract: We report x-ray photon correlation spectroscopy (XPCS) results on bidimensional (2D) gels formed by a Langmuir monolayer of gold nanoparticles. The system allows an experimental determination of the fourth order time correlation function, which is compared to the usual second order correlation function and to the mechanical response measured on macroscopic scale. The observed dynamics is anisotropic, heterogeneous and superdiffusive on the nanoscale. Different time scales, associated with fast heterogeneous dynamics inside 2D cages and slower motion of larger parts of the film, can be identified from the correlation functions. The XPCS results are discussed in view of other experimental results and models of three-dimensional gel dynamics.

Crossover in growth law and violation of superuniversality in the random-field Ising model.

Abstract: We study the nonconserved phase-ordering dynamics of the d=2,3 random-field Ising model, quenched to below the critical temperature. Motivated by the puzzling results of previous work in two and three dimensions, reporting a crossover from power-law to logarithmic growth, together with superuniversal behavior of the correlation function, we have undertaken a careful investigation of both the domain growth law and the autocorrelation function. Our main results are as follows: We confirm the crossover to asymptotic logarithmic behavior in the growth law, but, at variance with previous findings, we find the exponent in the preasymptotic power law to be disorder dependent, rather than being that of the pure system. Furthermore, we find that the autocorrelation function does not display superuniversal behavior. This restores consistency with previous results for the d=1 system, and fits nicely into the unifying scaling scheme we have recently proposed in the study of the random-bond Ising model.

Phase diagram of two-dimensional systems of dipole-like colloids

Abstract: Based on Discontinuous Molecular Dynamics (DMD) simulations we present a phase diagram of two-dimensional nano-particles with dipole-like short-ranged interactions. Similar to systems with true, long-ranged dipolar interactions the present system undergoes a transition from an isotropic fluid phase into a polymer-like fluid, characterized by an association of most particles into clusters. Further decrease of the temperature leads to a percolated system which, moreover, displays dynamical properties reminiscent of a gel. Specifically, we find a plateau in the mean-squared displacement and a non-gaussian behavior of the self-part of the van Hove correlation function. In the high density region we observe crystallization from the isotropic fluid into a solid phase with hexagonal order. Surprisingly, the crystallization is accompanied by a global parallel ordering of the dipole moments, i.e., a ferroelectric phase. This behavior is in marked contrast to what is found in 2D systems with long-ranged dipolar interactions. Our results allow insights into the design of gel-like or highly ordered structures at interfaces, shells around droplets and bubbles and new-sheet like materials.

Dynamic relaxation of a liquid cavity under amorphous boundary conditions

Abstract: The growth of cooperatively rearranging regions was invoked long ago by Adam and Gibbs to explain the slowing down of glass-forming liquids. The lack of knowledge about the nature of the growing order, though, complicates the definition of an appropriate correlation function. One option is the point-to-set (PTS) correlation function, which measures the spatial span of the influence of amorphous boundary conditions on a confined system. By using a swap Monte Carlo algorithm we measure the equilibration time of a liquid droplet bounded by amorphous boundary conditions in a model glass-former at low temperature, and we show that the cavity relaxation time increases with the size of the droplet, saturating to the bulk value when the droplet outgrows the point-to-set correlation length. This fact supports the idea that the point-to-set correlation length is the natural size of the cooperatively rearranging regions. On the other hand, the cavity relaxation time computed by a standard, nonswap dynamics, has the opposite behavior, showing a very steep increase when the cavity size is decreased. We try to reconcile this difference by discussing the possible hybridization between mode-coupling theory and activated processes, and by introducing a new kind of amorphous boundary conditions, inspired by the concept of frozen external state as an alternative to the commonly used frozen external configuration.

On the inadequacy of n-point correlation functions to describe nonlinear cosmological fields: explicit examples and connection to simulations

Abstract: Motivated by recent results on lognormal statistics showing that the moment hierarchy of a lognormal variable completely fails at capturing its information content in the large variance regime, in this work we discuss the inadequacy of the hierarchy of correlation functions to describe a correlated lognormal field, which provides a roughly accurate description of the nonlinear cosmological matter density field. We present families of fields having the same hierarchy of correlation functions than the lognormal field at all orders. This explicitly demonstrates the little studied though known fact that the correlation function hierarchy never provides a complete description of a lognormal field, and that it fails to capture information in the nonlinear regime, where other simple observables are left totally unconstrained. We discuss why perturbative, Edgeworth-like approaches to statistics in the nonlinear regime, common in cosmology, can never reproduce or predict that effect, and why it is, however, generic for tailed fields, hinting at a breakdown of the perturbation theory based on the field fluctuations. We make a rough but successful quantitative connection to N-body simulations results that showed that the spectrum of the log-density field carries more information than the spectrum of the field entering the nonlinear regime.

Mean Square Displacement and Reorientational Correlation Function in Entangled Polymer Melts Revealed by Field Cycling 1H and 2H NMR Relaxometry

Abstract: Mixtures of protonated and deuterated polybutadiene and polydimethylsiloxane are studied by means of field-cycling (FC) 1H NMR relaxometry in order to analyze the intra- and intermolecular contributions to spin–lattice relaxation. They reflect reorientational and translational dynamics,respectively. Master curves in the susceptibility representation χ″(ωτs) are constructed by employing frequency–temperature superposition with τs denoting the segmental correlation time. The intermolecular contribution is dominating at low frequencies and allows extracting the segmental mean square displacement ⟨R2(t)⟩, which reveals two power-law regimes. The one at short times agrees with t0.5 predicted for the free Rouse regime and at long times a lower exponent is observed in fair agreement with t0.25 expected for the constrained Rouse regime of the tube-reptation model. Concomitantly the reorientational rank-two correlation function C2(t/τs) is obtained from the intramolecular part. Again two power-law regimes t–e are ...

Using mutual information to measure order in model glass formers.

Abstract: Whether or not there is growing static order accompanying the dynamical heterogeneity and increasing relaxation times seen in glassy systems is a matter of dispute. An obstacle to resolving this issue is that the order is expected to be amorphous and so not amenable to simple order parameters. We use mutual information to provide a general measurement of order that is sensitive to multiparticle correlations. We apply this to two glass-forming systems (two-dimensional binary mixtures of hard disks with different size ratios to give varying amounts of hexatic order) and show that there is little growth of amorphous order in the system without crystalline order. In both cases we measure the dynamical length with a four-point correlation function and find that it increases significantly faster than the static lengths in the system as density is increased. We further show that we can recover the known scaling of the dynamic correlation length in a kinetically constrained model, the two-vacancy-assisted-hopping triangular lattice gas.

Statistical and systematic errors in redshift-space distortion measurements from large surveys

Abstract: We investigate the impact of statistical and systematic errors on measurements of linear redshift-space distortions (RSD) in future cosmological surveys, analyzing large catalogues of dark-matter halos from the BASICC simulation. These allow us to estimate the dependence of errors on typical survey properties, as volume, galaxy density and mass (i.e. bias factor) of the adopted tracer. We find that measures of the specific growth rate \beta=f/b using the Hamilton/Kaiser harmonic expansion of the redshift-space correlation function \xi(r_p,\pi) on scales larger than 3/h Mpc are typically under-estimated by up to 10% for galaxy sized halos. This is significantly larger than the corresponding statistical errors, which amount to a few percent, indicating the importance of non-linear improvements to the Kaiser model to obtain accurate measurements of the growth rate. We compare the statistical errors to predictions obtained with the Fisher information matrix, based on the usual FKP prescription for the errors on the power spectrum. We show that this produces parameter errors fairly similar to the standard deviations from the halo catalogues, but only if applied to strictly linear scales in Fourier space (k<0.2 h/Mpc). Finally, we present an accurate scaling formula describing the relative error on {\beta} as a function of the survey parameters, which closely matches the simulation results in all explored regimes. This provides a handy and plausibly more realistic alternative to the Fisher matrix approach, to quickly and accurately predict RSD statistical errors expected from future surveys.

Two-body momentum correlations in a weakly interacting one-dimensional Bose gas

Abstract: We analyze the two-body momentum correlation function for a uniform weakly interacting 1D Bose gas. We show that the strong positive correlation between opposite momenta, expected in a Bose-Einstein condensate with a true long-range order, almost vanishes in a phase fluctuating quasicondensate where the long-range order is destroyed. Using the Luttinger liquid approach, we derive an analytic expression for the momentum correlation function in the quasicondensate regime, showing: (i) the reduction and broadening of the opposite-momentum correlations (compared to the singular behaviour in a true condensate), and (ii) an emergence of anti-correlations at small momenta. We also numerically investigate the momentum correlations in the crossover between the quasicondensate and the ideal Bose gas regimes using a classical field approach and show how the anti-correlations gradually disappear in the ideal gas limit.

Signatures of charmonium modification in spatial correlation functions

Abstract: We study spatial correlation functions of charmonium in 2+1 flavor QCD using an improved staggered formulation. Contrary to the temporal correlation functions the spatial correlation functions exhibit a strong temperature dependence above the QCD transition temperature. Above this temperature they are sensitive to temporal boundary conditions. Both features become significant at a temperature close to 1.5Tc and suggest corresponding modifications of charmonium spectral functions.

Charge conservation and the shape of the ridge of two-particle correlations in relativistic heavy-ion collisions.

Abstract: We demonstrate that, in the framework of the event-by-event hydrodynamics followed by statistical hadronization, the proper charge conservation in the mechanism of hadron production provides the crucial nonflow component and leads to agreement with the two-dimensional two-particle correlation data in relative azimuthal angle and pseudorapidity at soft transverse momenta (p(T)<2 GeV). The falloff of the same-side ridge in relative pseudorapidity follows from the fact that a pair of particles with balanced charges is emitted from the same fluid element, whose collective velocity collimates the momenta of the pair. We reproduce basic experimental features of the two-dimensional correlation function, such as the dependence on the relative charge and centrality, as well as the related charge balance functions and the harmonic flow coefficients as functions of the relative pseudorapidity.

Analytical expressions for the log-amplitude correlation function for plane wave propagation in anisotropic non-Kolmogorov refractive turbulence.

Abstract: An analytical expression for the log-amplitude correlation function for plane wave propagation through anisotropic non-Kolmogorov turbulent atmosphere is derived. The closed-form analytic results are based on the Rytov approximation. These results agree well with wave optics simulation based on the more general Fresnel approximation as well as with numerical evaluations, for low-to-moderate strengths of turbulence. The new expression reduces correctly to the previously published analytic expressions for the cases of plane wave propagation through both nonisotropic Kolmogorov turbulence and isotropic non-Kolmogorov turbulence cases. These results are useful for understanding the potential impact of deviations from the standard isotropic Kolmogorov spectrum.

On the inadequacy of N-point correlation functions to describe nonlinear cosmological fields: explicit examples and connection to simulations

Abstract: Motivated by recent results on lognormal statistics showing that the moment hierarchy of a lognormal variable completely fails at capturing its information content in the large variance regime, we discuss in this work the inadequacy of the hierarchy of correlation functions to describe a correlated lognormal field, which provides a roughly accurate description of the non-linear cosmological matter density field. We present families of fields having the same hierarchy of correlation functions than the lognormal field at all orders. This explicitly demonstrates the little studied though known fact that the correlation function hierarchy never provides a complete description of a lognormal field, and that it fails to capture information in the non-linear regime, where other simple observables are left totally unconstrained. We discuss why perturbative, Edgeworth-like approaches to statistics in the non-linear regime, common in cosmology, can never reproduce or predict that effect, and why it is however generic for tailed fields, hinting at a breakdown of the perturbation theory based on the field fluctuations. We make a rough but successful quantitative connection to N-body simulations results, that showed that the spectrum of the log-density field carries more information than the spectrum of the field entering the non-linear regime.

New approximate solution for N-point correlation functions for heterogeneous materials

Abstract: Statistical N -point correlation functions are used for calculating properties of heterogeneous systems. The strength and the main advantage of the statistical continuum approach is the direct link to statistical information of microstructure. Two-point correlation functions are the lowest order of correlation functions that can describe the morphology and the microstructure-properties relationship. Experimentally, statistical pair correlation functions are obtained using SEM or small x-ray scattering techniques. Higher order correlation functions must be calculated or measured to increase the precision of the statistical continuum approach. To achieve this aim a new approximation methodology is utilized to obtain N -point correlation functions for non-FGM (functional graded materials) heterogeneous microstructures. Conditional probability functions are used to formulate the proposed theoretical approximation. In this approximation, weight functions are used to connect subsets of ( N −1)-point correlation functions to estimate the full set of N -point correlation function. For the approximation of three and four point correlation functions, simple weight functions have been introduced. The results from this new approximation, for three-point probability functions, are compared to the real probability functions calculated from a computer generated three-phase reconstructed microstructure in three-dimensional space. This three-dimensional reconstruction was based on an experimental two-dimensional microstructure (SEM image) of a three-phase material. This comparison proves that our new comprehensive approximation is capable of describing higher order statistical correlation functions with the needed accuracy.

Angular correlation functions of X-ray point-like sources in the full exposure XMM-LSS field

Abstract: Aims. Our aim is to study the large-scale structure of different types of AGN using the medium-deep XMM-LSS survey. Methods. We measure the two-point angular correlation function of ∼5700 and 2500 X-ray point-like sources over the ∼11 sq. deg. XMM-LSS field in the soft (0.5–2 keV) and hard (2–10 keV) bands. For the conversion from the angular to the spatial correlation function we used the Limber integral equation and the luminosity-dependent density evolution model of the AGN X-ray luminosity function. Results. We have found significant angular correlations with the power-law parameters γ = 1.81 ± 0.02, θ0 = 1.3 �� ± 0.2 �� for the soft, and γ = 2.00 ± 0.04, θ0 = 7.3 �� ± 1.0 �� for the hard bands. The amplitude of the correlation function w(θ) is higher in the hard than in the soft band for fx < 10 −14 erg s −1 cm −2 and lower above this flux limit. We confirm that the clustering strength θ0 grows with the flux limit of the sample, a trend which is also present in the amplitude of the spatial correlation function, but only for the soft band. In the hard band, it remains almost constant with r0 � 10 h −1 Mpc, irrespective of the flux limit. Our analysis of AGN subsamples with different hardness ratios shows that the sources with a hard-spectrum are more clustered than soft-spectrum ones. This result may be a hint that the two main types of AGN populate different environments. Finally, we find that our clustering results correspond to an X-ray selected AGN bias factor of ∼2.5 for the soft band sources (at a median ¯ � 1.1) and ∼3.3 for the hard band sources (at a median ¯ ,

Behavior of the anomalous correlation function in a uniform two-dimensional Bose gas

Abstract: We investigate the behavior of the anomalous correlation function in two-dimensional Bose gas In the local case, we find that this quantity has a finite value in the limit of weak interactions at zero temperature The effects of the anomalous density on some thermodynamic quantities are also considered These effects can modify, in particular, the chemical potential, the ground-state energy, the depletion, and the superfluid fraction Our predictions are in good agreement with recent analytical and numerical calculations We show also that the anomalous density presents a significant importance compared to the noncondensed one at zero temperature The single-particle anomalous correlation function is expressed in two-dimensional homogenous Bose gases by using the density-phase fluctuation We then confirm that the anomalous average accompanies in analogous manner the true condensate at zero temperature, while it does not exist at finite temperature

Minimizing the frequency correlation of photon pairs in photonic crystal fibers

Abstract: Based on the dispersion property of a given photonic crystal fiber (PCF), we study how to directly generate photon pairs with minimized frequency correlation via pulse-pumped spontaneous four-wave mixing. After illustrating why the intensity correlation function g(2) of individual signal (idler) photons can be used to reliably characterize the frequency correlation of photon pairs, we numerically investigate the dependence of g(2) under various kinds of experimental conditions. The results show that to minimize the frequency correlation, the experimental parameters should be properly optimized by balancing the influences of the high-order dispersion and the intrinsic sinc oscillation of phase matching function, apart from the satisfaction of the specified phase matching condition and the usage of transform-limited pump pulses. To verify the calculated results, we conduct two series of experiments by regulating the pump to respectively satisfy the asymmetric and symmetric group velocity matching conditions in our 0.6 m-long PCF. In both cases, the measured values of g(2) are less than the calculated results due to the inhomogeneity of the PCF; however, the experimental results qualitatively agree with the numerical simulations. Our investigation is very useful in fiber-based quantum state engineering.

Description and reconstruction of the soil pore space using correlation functions

Abstract: In this paper a method for the description and reconstruction of the soil pore space using correlation functions has been examined. The reconstruction procedure employed here is the best way of verification of the potential descriptor of the soil pore space. Thin sections representing eight major types of pore space in zonal loamy soils and parent materials of the Russian Plain with pores of different shapes and orientations have been chosen for this study. Comparison based on the morphological analysis of the original pore space images and their correlation function reconstructions obtained using simulated annealing technique indicates that this method of reconstruction adequately describes the isometric soil pore space with isometric dissected, isometric slightly dissected, and rounded pores. The two-point correlation functions calculated with the use of the orthogonal method proved to be different for the examined types of soil pore space; they reflect the soil porosity, specific surface, and pore structure correlations at different lengths. The results of this study allow us to conclude that the description of the soil pore space with the help of correlation functions is a promising approach, but requires more development. Further directions of the development of this method for describing the soil pore space and determining the soil physical processes are outlined.

Fluctuations and micro-heterogeneity in aqueous mixtures

Abstract: The problem as to why water-water density correlations are systematically overestimated in computer simulation of aqueous mixtures is examined through an extensive molecular dynamics study of mixtures of the extended single point charge water model with a fully miscible weaker version of it, obtained by scaling down the site partial charges by a factor 2/3, thereby eliminating solute-solvent size differences. The study reveals that enhanced water correlations is a genuine physical effect, and are not an artifact of the simulations or the models, as previously suggested in the context of realistic aqueous mixtures. Rather, they correspond to the existence of strongly correlated water domains, for “weak-water” mole fraction x > 0.4, that modulate the spatial decay of the density correlations. These domains produce a prepeak in the structure factor, suggesting that simple aqueous mixture might behave just like micro-emulsions. The overestimated long range water correlations result from incorrect predictions of the asymptote of these correlations, which themselves arise from size limitations of the simulation box. However, by requiring consistency between thermodynamical and structural expressions of the concentration fluctuations, a method to predict the proper decay of the correlation function is obtained herein, inspired by the formal analogy with micro-emulsions. This study provides a new insight for the large values of the experimental Kirkwood-Buff integrals for many aqueous mixtures: these mixtures are in a Lifshitz-type regime, where concentration fluctuations compete with water domain formation.

Nonequilibrium dynamics of bosonic Mott insulators in an electric field

Abstract: We study the nonequilibrium dynamics of one-dimensional Mott-insulating bosons in the presence of a tunable effective electric field e which takes the system across a quantum critical point separating a disordered and a translation symmetry broken ordered phase. We provide an exact numerical computation of the residual energy Q, the log fidelity F, the defect density D/L, and the order parameter correlation function for a linear-in-time variation of E with a rate v. We discuss the temporal and spatial variation of these quantities for a range of v and for finite system sizes as relevant to realistic experimental setups [ J. Simon et al. Nature (London) 472 307 (2011)]. We show that in finite-sized systems Q, F, and D obey Kibble-Zurek scaling, and suggest further experiments within this setup to test our theory.

Superaging correlation function and ergodicity breaking for Brownian motion in logarithmic potentials

Abstract: We consider an overdamped Brownian particle moving in a confining asymptotically logarithmic potential, which supports a normalized Boltzmann equilibrium density. We derive analytical expressions for the two-time correlation function and the fluctuations of the time-averaged position of the particle for large but finite times. We characterize the occurrence of aging and nonergodic behavior as a function of the depth of the potential, and we support our predictions with extensive Langevin simulations. While the Boltzmann measure is used to obtain stationary correlation functions, we show how the non-normalizable infinite covariant density is related to the superaging behavior.

Positive- P phase-space-method simulation of superradiant emission from a cascade atomic ensemble

Abstract: The superradiant emission properties from an atomic ensemble with cascade level configuration is numerically simulated. The correlated spontaneous emissions (signal then idler fields) are purely stochastic processes which are initiated by quantum fluctuations. We utilize the positive-$P$ phase-space method to investigate the dynamics of the atoms and counterpropagating emissions. The light field intensities are calculated, and the signal-idler correlation function is studied for different optical depths of the atomic ensemble. A shorter correlation time scale for a denser atomic ensemble implies a broader spectral window needed to store or retrieve the idler pulse.

Early-time velocity autocorrelation for charged particles diffusion and drift in static magnetic turbulence

Abstract: Using test-particle simulations, we investigate the temporal dependence of the two-point velocity correlation function for charged particles scattering in a time-independent spatially fluctuating magnetic field derived from a three-dimensional isotropic turbulence power spectrum. Such a correlation function allowed us to compute the spatial coefficients of diffusion both parallel and perpendicular to the average magnetic field. Our simulations confirm the dependence of the perpendicular diffusion coefficient on turbulence energy density and particle energy predicted previously by a model for early-time charged particle transport. Using the computed diffusion coefficients, we exploit the particle velocity autocorrelation to investigate the timescale over which the particles "decorrelate" from the solution to the unperturbed equation of motion. Decorrelation timescales are evaluated for parallel and perpendicular motions, including the drift of the particles from the local magnetic field line. The regimes of strong and weak magnetic turbulence are compared for various values of the ratio of the particle gyroradius to the correlation length of the magnetic turbulence. Our simulation parameters can be applied to energetic particles in the interplanetary space, cosmic rays at the supernova shocks, and cosmic-rays transport in the intergalactic medium.

Spin-alignment echo NMR: probing Li+ hopping motion in the solid electrolyte Li7La3Zr2O12 with garnet-type tetragonal structure.

Abstract: 7Li spin-alignment echo (SAE) nuclear magnetic resonance (NMR) spectroscopy has been used to measure single-spin hopping correlation functions of polycrystalline Li7La3Zr2O12. Damping of the echo amplitude S2(tm,tp), recorded at variable mixing time tm but fixed preparation time tp, turns out to be solely controlled by slow Li jump processes taking place in the garnet-like structure. The decay rates directly obtained by parametrizing the curves S2(tm,tp) with stretched exponential functions show Arrhenius behaviour pointing to an activation energy of approximately 0.5 eV. This value, probed by employing an atomic-scale NMR method, is in very good agreement with that deduced from impedance spectroscopy used to measure macroscopic Li transport parameters. Most likely, the two methods are sensitive to the same hopping correlation function although Li dynamics are probed in a quite different manner.