Effects Of Long-range Correlations Research Articles

Single-chain simulation of Ising density functional theory for weak polyelectrolytes.

Conventional theories of weak polyelectrolytes are either computationally prohibitive to account for the multidimensional inhomogeneity of polymer ionization in a liquid environment or oversimplistic in describing the coupling effects of ion-explicit electrostatic interactions and long-range intrachain correlations. To bridge this gap, we implement the Ising density functional theory (iDFT) for ionizable polymer systems using the single-chain-in-mean-field algorithm. The single-chain-in-iDFT (sc-iDFT) shows significant improvements over conventional mean-field methods in describing segment-level dissociation equilibrium, specific ion effects, and long-range intrachain correlations. With an explicit consideration of the fluctuations of polymer configurations and the position-dependent ionization of individual polymer segments, sc-iDFT provides a faithful description of the structure and thermodynamic properties of inhomogeneous weak polyelectrolyte systems across multiple length scales.

Plasma screening and the critical end point in the QCD phase diagram

In heavy-ion collisions, fluctuations of conserved charges are known to be sensitive observables to probe criticality for the QCD phase transition and to locate the position of the putative critical end point (CEP). In this work we seek to show that the Linear Sigma Model with quarks produces an effective description of the QCD phase diagram in which deviations from a Hadron Resonance Gas are due to plasma screening effects, encoded in the contribution of the ring diagrams. Accounting for these, it is possible to include in the description the effect of long-range correlations. To set the model parameters we use LQCD results for the crossover transition at vanishing chemical potential. Finally, studying baryon number fluctuations from the model, we show that the CEP can be located within the HADES and/or the lowest end of the NICA energy domain, √ sNN ∼ 2 GeV.

Effects of critical correlations on quantum percolation in two dimensions

We analyze the out-of-equilibrium dynamics of a quantum particle coupled to local magnetic degrees of freedom that undergo a classical phase transition. Specifically, we consider a two-dimensional tight-binding model that interacts with a background of classical spins in thermal equilibrium, which are subject to Ising interactions and act as emergent, correlated disorder for the quantum particle. Particular attention is devoted to temperatures close to the ferromagnet-to-paramagnet transition. To capture the salient features of the classical transition, namely the effects of long-range correlations, we focus on the strong coupling limit, in which the model can be mapped onto a quantum percolation problem on spin clusters generated by the Ising model. By inspecting several dynamical probes such as energy level statistics, inverse participation ratios, and wave-packet dynamics, we provide evidence that the classical phase transition might induce a delocalization-localization transition in the quantum system at certain energies. We also identify further important features due to the presence of Ising correlations, such as the suppression of compact localized eigenstates.

Effects of Short and Long Range Correlations on the Charge Densities and Radii of Ca Nuclei

The experimental data for the charge (proton) density differences of the even Ca nuclei is analyzed by means of a simple phenomenological model where the effects of certain type short and long range correlations have been accounted. Short range correlations are approximated through the Jastrow type correlation function while for long range correlations the fluctuations of the nuclear surface are considered. The analysis shows that the combined effects of these correlations lead to a better description of the experimental charge (proton) density differences. Moreover, the calculated charge mean square radii of the even Ca nuclei exhibit a parabolic behaviour and compare well with the experimental isotope shifts from the laser spectroscopy measurements.

Forbidden transitions in neutral- and charged-current interactions between low-energy neutrinos and argon

Background: The study of low-energy neutrinos and their interactions with atomic nuclei is crucial to several open problems in physics, including the neutrino mass hierarchy, CP-violation, candidates of Beyond Standard Model physics and supernova dynamics. Examples of experiments include CAPTAIN at SNS as well as DUNE's planned detection program of supernova neutrinos. Purpose: We present cross section calculations for quasielastic charged current and neutral current neutrinos at low energies, with a focus on $^{40}$Ar. We also take a close look at pion decay-at-rest neutrino spectra, which are used in e.g. the SNS experiment at Oakridge. Method and results: We employ a Hartree Fock + Continuum Random Phase Approximations (HF+CRPA) framework, which allows us to model the responses and include the effects of long-range correlations. It is expected to provide a good framework to calculate forbidden transitions, whose contribution which we show to be non-negligible. Conclusions: Forbidden transitions can be expected to contribute sizeably to the reaction strength at typical low-energy kinematics, such as DAR neutrinos. Modeling and Monte Carlo simulations need to take all due care to account for the influence of their contributions.

Subdiffusive Lévy flights in quantum nonlinear Schrödinger lattices with algebraic power nonlinearity.

We report a theoretical result concerning the dynamics of an initially localized wave packet in quantum nonlinear Schrödinger lattices with a disordered potential. A class of nonlinear lattices with subquadratic power nonlinearity is considered. We show that there exists a parameter range for which an initially localized wave packet can spread along the lattice to unlimited distances, but the phenomenon is purely quantum and is hindered in the corresponding classical lattices. The mechanism for this spreading is moreover very peculiar and assumes that the components of the wave field may form coupled states by tunneling under the topological barriers caused by multiple discontinuities in the operator space. Then these coupled states thought of as quasiparticle states can propagate to long distances on Lévy flights with a distribution of waiting times. The overall process is subdiffusive and occurs as a competition between long-distance jumps of the quasiparticle states, on the one hand, and long-time trapping phenomena mediated by clustering of unstable modes in wave number space, on the other hand. The kinetic description of the transport, discussed in this work, is based on fractional-derivative equations allowing for both (i) non-Markovianity of the spreading process as a result of attractive interaction among the unstable modes; this interaction is then described in terms of the familiar Lennard-Jones potential; and (ii) the effect of long-range correlations in wave number space tending to introduce fast channels for the transport, the so-called "stripes." We argue that the notion of stripes is key to understand the topological constraints behindthequantum spreading, and we involve the idea of stripy ordering to obtain self-consistently the parameters of the associated waiting-time and jump-length distributions. Finally, we predict the asymptotic laws for quantum transport and show that the relevant parameter determining these laws is the exponent of the power law defining the type of the nonlinearity. The results presented here shed light on the origin of Lévy flights in quantum nonlinear lattices with disorder.

Entropy measures, entropy estimators, and their performance in quantifying complex dynamics: Effects of artifacts, nonstationarity, and long-range correlations.

Entropy measures are widely applied to quantify the complexity of dynamical systems in diverse fields. However, the practical application of entropy methods is challenging, due to the variety of entropy measures and estimators and the complexity of real-world time series, including nonstationarities and long-range correlations (LRC). We conduct a systematic study on the performance, bias, and limitations of three basic measures (entropy, conditional entropy, information storage) and three traditionally used estimators (linear, kernel, nearest neighbor). We investigate the dependence of entropy measures on estimator- and process-specific parameters, and we show the effects of three types of nonstationarities due to artifacts (trends, spikes, local variance change) in simulations of stochastic autoregressive processes. We also analyze the impact of LRC on the theoretical and estimated values of entropy measures. Finally, we apply entropy methods on heart rate variability data from subjects in different physiological states and clinical conditions. We find that entropy measures can only differentiate changes of specific types in cardiac dynamics and that appropriate preprocessing is vital for correct estimation and interpretation. Demonstrating the limitations of entropy methods and shedding light on how to mitigate bias and provide correct interpretations of results, this work can serve as a comprehensive reference for the application of entropy methods and the evaluation of existing studies.

A n-vector model for charge transport in molecular semiconductors.

We develop a lattice model utilizing coarse-grained molecular sites to study charge transport in molecular semiconducting materials. The model bridges atomistic descriptions and structureless lattice models by mapping molecular structure onto sets of spatial vectors isomorphic with spin vectors in a classical n-vector Heisenberg model. Specifically, this model incorporates molecular topology-dependent orientational and intermolecular coupling preferences, including the direct inclusion of spatially correlated transfer integrals and site energy disorder. This model contains the essential physics required to explicitly simulate the interplay of molecular topology and correlated structural disorder, and their effect on charge transport. As a demonstration of its utility, we apply this model to analyze the effects of long-range orientational correlations, molecular topology, and intermolecular interaction strength on charge motion in bulk molecular semiconductors.

Relaxation of ferroelectric states in 2D distributions of quantum dots: EELS simulation

The relaxation time of collective electronic states in a 2D distribution of quantum dots is investigated theoretically by simulating EELS experiments. From the numerical calculation of the probability of energy loss of an electron beam, traveling parallel to the distribution, it is possible to estimate the damping time of ferroelectric-like states. We generate this collective response of the distribution by introducing a mean field interaction among the quantum dots, and then, the model is extended incorporating effects of long-range correlations through a Bragg–Williams approximation. The behavior of the dielectric function, the energy loss function, and the relaxation time of ferroelectric-like states is then investigated as a function of the temperature of the distribution and the damping constant of the electronic states in the single quantum dots. The robustness of the trends and tendencies of our results indicate that this scheme of analysis can guide experimentalists to develop tailored quantum dots distributions for specific applications.

Identification of Nuclear Effects in Neutrino-Carbon Interactions at Low Three-Momentum Transfer.

Two different nuclear-medium effects are isolated using a low three-momentum transfer subsample of neutrino-carbon scattering data from the MINERvA neutrino experiment. The observed hadronic energy in charged-current ν_{μ} interactions is combined with muon kinematics to permit separation of the quasielastic and Δ(1232) resonance processes. First, we observe a small cross section at very low energy transfer that matches the expected screening effect of long-range nucleon correlations. Second, additions to the event rate in the kinematic region between the quasielastic and Δ resonance processes are needed to describe the data. The data in this kinematic region also have an enhanced population of multiproton final states. Contributions predicted for scattering from a nucleon pair have both properties; the model tested in this analysis is a significant improvement but does not fully describe the data. We present the results as a double-differential cross section to enable further investigation of nuclear models. Improved description of the effects of the nuclear environment are required by current and future neutrino oscillation experiments.

Fluctuations in interacting particle systems with memory

We consider the effects of long-range temporal correlations in many-particle systems, focusing particularly on fluctuations about the typical behaviour. For a specific class of memory dependence we discuss the modification of the large deviation principle describing the probability of rare currents and show how superdiffusive behaviour can emerge. We illustrate the general framework with detailed calculations for a memory-dependent version of the totally asymmetric simple exclusion process as well as indicating connections to other recent work.

Influence of the fiber geometry on the macroscopic elastic and thermal properties

This work focuses on the linear elastic and thermal properties of real and virtual, computer-generated fibrous composites. A stochastic microstructure model is used to generate densely-assembled 3D systems of curved, non overlapping fibers with specific orientation distributions. This model is first optimized to approach the characteristics of a real fiber glass polymer by fitting geometrical and statistical parameters, such as fiber orientation, radius, length, and curvature. Second, random realizations of the stochastic models that depart from the characteristics of the fiber glass polymer are generated. The latter, which range from isotropic to transversely isotropic and to orthotropic materials, represent plausible virtual fibrous materials. Full-field numerical computations, undertaken by means of the Fourier-based (FFT) method, are used to estimate the local and effective mechanical and thermal responses of the fibrous composites. The anisotropy of the macroscopic responses as well as the size of the corresponding representative volume element (RVE) are examined numerically. It is found that the variance of the properties on a volume V scales as a powerlaw ∼1/Vα where α<1, an effect of long-range correlations in the microstructure. Finally, the overall behavior of the fiber composites are computed for varying fiber curvature and orientation distributions, and compared with available analytical bounds. We find that the fiber arrangement strongly influences the elastic and thermal responses, less so for the fiber curvature.

Effect of long-range spatial correlations on the lifetime statistics of an emitter in a two-dimensional disordered lattice

The effect of spatial correlations on the Purcell effect in a bidimensional dispersion of resonant nanoparticles is analyzed. We perform extensive calculations on the fluorescence decay rate of a point emitter embedded in a system of nanoparticles statistically distributed according to a simple 2D lattice-gas model near the critical point. For short-range correlations (high temperature thermalization) the Purcell factors present a long-tailed statistic which evolves towards a bimodal distribution when approaching the critical point where the spatial correlation length diverges. Our results suggest long-range correlations as a possible origin of the large fluctuations of experimental decay rates in disordered metal films.

Composites with fractal microstructure: The effect of long range correlations on elastic–plastic and damping behavior

The effect of correlations of the spatial distribution of inclusions in a two-phase composite is studied numerically in this work. Microstructures with fractal distribution of inclusions, characterized by long-range power law correlations, are compared with random inclusion distributions of same volume fraction. The elastic–plastic response of composites with stiff elastic inclusions and elastic–plastic matrix is studied, and it is concluded that fractal microstructures always lead to stiffer composites, with higher strain hardening rates, compared with the equivalent composites with randomly distributed inclusions. Composites with filler distributions characterized by shorter range, exponential correlations exhibit behavior intermediate between that of random and power law-correlated microstructures. Larger variability from replica to replica is observed in the fractal case. The pressure in inclusions is larger in the case of fractal microstructures, indicating that these are expected to be advantageous in applications such as toughening of thermoset polymers which takes place via the cavitation mechanism. The effect of the spatial distribution of inclusions on the effective damping of the composite is also investigated. The matrix is considered elastic and non-dissipative, while inclusions dissipate energy. The composite with fractal microstructure provides more damping than the random microstructure of same filler volume fraction, and the effect increases with increasing fractal dimension. When damping is introduced only in the interfaces between matrix and inclusions, the spatial distribution of fillers becomes inconsequential for the overall composite behavior. These results are relevant for the design of composites with hierarchical multiscale structure.

Decay of Batchelor and Saffman rotating turbulence

The decay rate of isotropic and homogeneous turbulence is known to be affected by the large-scale spectrum of the initial perturbations, associated with at least two canonical self-preserving solutions of the von Kármán-Howarth equation: the so-called Batchelor and Saffman spectra. The effect of long-range correlations in the decay of anisotropic flows is less clear, and recently it has been proposed that the decay rate of rotating turbulence may be independent of the large-scale spectrum of the initial perturbations. We analyze numerical simulations of freely decaying rotating turbulence with initial energy spectra ∼k^{4} (Batchelor turbulence) and ∼k^{2} (Saffman turbulence) and show that, while a self-similar decay can not be identified for the total energy, the decay is indeed affected by long-range correlations. The decay of two- and three-dimensional modes follows distinct power laws in each case, which are consistent with predictions derived from the anisotropic von Kármán-Howarth equation, and with conservation of anisotropic integral quantities by the flow evolution.

Delocalization to localization transition in one-dimensional systems with long-range correlated off-diagonal disorder

The combined effects of long-range correlations and disorder strength on critical properties of electronic states in one-dimensional systems with long-range correlated off-diagonal disorder are investigated for the whole energy band. Numerical studies on the localization length demonstrate the existence of disorder-induced delocalization-to-localization transition (DLT) and energy-induced DLT in such systems when the correlations of hopping terms are strong enough to generate extended states. Further calculations confirm that the critical disorder strength and critical energy related to these DLTs are Wc=2t0−|E| and ±Ec=±|2t0−W|, respectively. Based on these critical points, the detailed phase diagrams in different parameter spaces are obtained.

Fault slip distribution and fault roughness

SUMMARY We present analysis of the spatial correlations of seismological slip maps and fault topography roughness, illuminating their identical self-affine exponent. Though the complexity of the coseismic spatial slip distribution can be intuitively associated with geometrical or stress heterogeneities along the fault surface, this has never been demonstrated. Based on new measurements of fault surface topography and on statistical analyses of kinematic inversions of slip maps, we propose a model, which quantitatively characterizes the link between slip distribution and fault surface roughness. Our approach can be divided into two complementary steps: (i) Using a numerical computation, we estimate the influence of fault roughness on the frictional strength (pre-stress). We model a fault as a rough interface where elastic asperities are squeezed. The Hurst exponent Hτ, characterizing the self-affinity of the frictional strength field, approaches Hτ = H// −1, where H// is the roughness exponent of the fault surface in the direction of slip. (ii) Using a quasi-static model of fault propagation, which includes the effect of long-range elastic interactions and spatial correlations in the frictional strength, the spatial slip correlation is observed to scale as Hs = Hτ + 1, where Hs represents the Hurst exponent of the slip distribution. Under the assumption that the origin of the spatial fluctuations in frictional strength along faults is the elastic squeeze of fault asperities, we show that self-affine geometrical properties of fault surface roughness control slip correlations and that Hs = H//. Given that H// = 0.6 for a wide range of faults (various accumulated displacement, host rock and slip movement), we predict that Hs = 0.6. Even if our quasi-static fault model is more relevant for creeping faults, the spatial slip correlations observed are consistent with those of seismological slip maps. A consequence is that the self-affinity property of slip roughness may be explained by fault geometry without considering dynamical effects produced during an earthquake.

CMS ridge effect at LHC as a manifestation of bremsstrahlung of gluons off quarks accelerated in a strong color field

The recently reported effect of long-range near-side angular correlations at LHC occurs for large multiplicities of particles with 1 GeV<p T <3 GeV. To understand the effect several possibilities have been discussed. In the letter we propose a simple qualitative mechanism which corresponds to gluon bremsstrahlung of quarks moving with acceleration defined by the string tension. The smallness of azimuthal angle difference Δφ along with large Δη at large multiplicities in this interval of p T are natural in this mechanism. The mechanism predicts also bremsstrahlung photons with mean values of p T ≈2.9 and 0.72 GeV.

Effects of Long-Range Correlations on Nonmagnetic Mott Transitions in Hubbard Model on Square Lattice

The mechanism of Mott transition in the Hubbard model on the square lattice is studied without explicit introduction of magnetic and superconducting correlations, using a variational Monte Carlo method. In the trial wave functions, we consider various types of binding factors between a doubly-occupied site (doublon, D) and an empty site (holon, H), like a long-range type as well as a conventional nearest-neighbor type, and add independent long-range D-D (H-H) factors. It is found that a wide choice of D-H binding factor leads to Mott transitions at critical values near the band width. We renew the D-H binding picture of Mott transitions by introducing two characteristic length scales, the D-H binding length l_{DH} and the minimum D-D distance l_{DD}, which we appropriately estimate. A Mott transition takes place at l_{DH}=l_{DD}. In the metallic regime (l_{DH}>l_{DD}), the domains of D-H pairs overlap with one another, thereby doublons and holons can move independently by exchanging the partners one after another. In contrast, the D-D factors give only a minor contribution to the Mott transition.

Fractality of eroded coastlines of correlated landscapes

Using numerical simulations of a simple sea-coast mechanical erosion model, we investigate the effect of spatial long-range correlations in the lithology of coastal landscapes on the fractal behavior of the corresponding coastlines. In the model, the resistance of a coast section to erosion depends on the local lithology configuration as well as on the number of neighboring sea sides. For weak sea forces, the sea is trapped by the coastline and the eroding process stops after some time. For strong sea forces erosion is perpetual. The transition between these two regimes takes place at a critical sea force, characterized by a fractal coastline front. For uncorrelated landscapes, we obtain, at the critical value, a fractal dimension D=1.33, which is consistent with the dimension of the accessible external perimeter of the spanning cluster in two-dimensional percolation. For sea forces above the critical value, our results indicate that the coastline is self-affine and belongs to the Kardar-Parisi-Zhang universality class. In the case of landscapes generated with power-law spatial long-range correlations, the coastline fractal dimension changes continuously with the Hurst exponent H, decreasing from D=1.34 to 1.04, for H=0 and 1, respectively. This nonuniversal behavior is compatible with the multitude of fractal dimensions found for real coastlines.