Fluctuations in fluids out of thermal equilibrium

After a brief review of dynamic correlations in equilibrium fluids, we consider the long-range correlations between the fluctuations in a fluid subjected to a large stationary temperature gradient. These long-range correlations enhance and modify the Rayleigh spectrum of the fluid. We elucidate that the modifications of the Rayleigh line are determined by the coupling of the entropy fluctuations to the transverse velocity fluctuations. Recent attempts to test the theoretical predictions with the aid of light-scattering experiments are discussed.     

Classical Coulomb systems: Screening and correlations revisited

From the laws of macroscopic electrostatics of conductors (in particular, the existence of screening), taken as given, one can deduce universal properties for the thermal fluctuations in a classical Coulomb system at equilibrium. The universality is especially apparent in the long-range correlations of the electrical potentials and fields. The charge fluctuations are derived from the field fluctuations. This is a convenient way to study the surface charge fluctuations on a conductor with boundaries. Explicit results are given for simple geometries. The potentials and the fields have Gaussian fluctuations, except for a short-distance cutoff.laboratory associated with the Centre National de la Recherche Scientifique.     

Random field effects in classical and quantum critical phenomena

The effect of quenched random fields on classical and quantum critical behaviour is studied by means of the ?-analysis for a number of systems. The investigation is performed in terms of a generalized random-field correlation function. The interplay of short-range correlations as well as of a parameter-dependent variety of long-range correlations with thermal and quantum fluctuations is revealed.     

Magnetic moments contribution to the specific heat and susceptibility of heavy fermion system

In non-magnetic heavy fermion systems, valence fluctuations prevent formation of long-range magnetic correlations. The RKKY exchange fields fluctuate due to f-electron transfers to the conduction band. To simulate these processes, we use the Ising-type model with fluctuating fields. The linear temperature dependence of the specific heat and temperature independence of susceptibility suggest that the f-electron contribution to these quantities can be considered as complementary to the one originating from Kondo resonance.     

Long-range strain correlations in sheared colloidal glasses

Glasses behave as solids on experimental time scales due to their slow relaxation. Growing dynamic length scales due to cooperative motion of particles are believed to be central to this slow response. For quiescent glasses, however, the size of the cooperatively rearranging regions has never been observed to exceed a few particle diameters, and the observation of long-range correlations has remained elusive. Here, we provide direct experimental evidence of long-range correlations during the deformation of a dense colloidal glass. By imposing an external stress, we force structural rearrangements, and we identify long-range correlations in the fluctuations of microscopic strain and elucidate their scaling and spatial symmetry. The applied shear induces a transition from homogeneous to inhomogeneous flow at a critical shear rate, and we investigate the role of strain correlations in this transition.     

Self-similarity of electrostatic fluctuations in a linear magnetised plasma system

In this Letter the long-range time correlations present in the fluctuation data in presence of electrostatic instability in a magnetised dc discharge plasma is presented. The electrostatic instability is generated due to the effect of crossed electric and magnetic field (E×B flow) and has intermediate frequency ranging from 50 to 100 MHz. Hurst exponent, the self-similarity parameter is calculated with the help of different statistical methods suggested by many researchers to determine the long-range time correlation present in fluctuation dynamics in the plasma column. The fluctuation in the ion saturation current is measured by a Langmuir probe for the study and the measurement is done both radially and axially in the plasma system. Estimated results clearly expose the self-similar character of the fluctuations with self-similarity parameters having values from 0.65 to 0.90 through the presence of long-range time correlation.     

Finite-size effects on intensity correlations in random media

The correlations between waves transmitted through random media are analyzed by use of a random-matrix approach and numerical simulations of rough waveguides. Although the intensity and conductance fluctuations are practically independent of the sample length, the correlations present a strong dependence on the length of the disordered region. In waveguide geometries the long-range correlations C((2)) and C((3)), usually associated to intensity and conductance fluctuations, respectively, become negative as the length of the system decreases. Our results provide a new interpretation of recent optical experiments on disordered slab geometries.     

Going beyond the self-consistent mean-field with the symmetry-restored generator coordinate method

Starting from successful self-consistent mean-field models, this paper discusses why and how to go beyond the mean field approximation. To include long-range correlations from fluctuations in collective degrees of freedom, one has to consider symmetry restoration and configuration mixing, which give access to ground-state correlations and spectroscopy.     

Equilibrium properties of classical systems with long-range forces. BBGKY equation,neutrality, screening,and sum rules

We introduce a generalization of the BBGKY equation to define the equilibrium states for systems with long-range forces and study the properties of such states. We show that there are properties typical of short-range forces (shape independence, normal fluctuations, asymptotic behavior of correlation functions) and others which are typical of long-range forces (possible shape dependence, neutrality, sum rules and screening, abnormal fluctuations, boundedness of the internal electric field). If the force decreases at infinity faster than the Coulomb force, the properties will be those typical of short-range forces; on the other hand, if the force decreases at infinity as the Coulomb force or slower, the properties will be those typical of long-range forces.     

Turbulentlike fluctuations in quasistatic flow of granular media

We analyze particle velocity fluctuations in a simulated granular system subjected to homogeneous quasistatic shearing. We show that these fluctuations share the following scaling characteristics of fluid turbulence in spite of their different physical origins: (i) scale-dependent probability distribution with non-Gaussian broadening at small time scales; (ii) spatial power spectrum of the velocity field showing a power-law decay, reflecting long-range correlations and the self-affine nature of the fluctuations; and (iii) superdiffusion of particles with respect to the mean background flow.     

Asymmetric multifractal scaling behavior in the Chinese stock market: Based on asymmetric MF-DFA

We utilized asymmetric multifractal detrended fluctuation analysis in this study to examine the asymmetric multifractal scaling behavior of Chinese stock markets with uptrends or downtrends. Results show that the multifractality degree of Chinese stock markets with uptrends is stronger than that of Chinese stock markets with downtrends. Correlation asymmetries are more evident in large fluctuations than in small fluctuations. By discussing the source of asymmetric multifractality, we find that multifractality is related to long-range correlations when the market is going up, whereas it is related to fat-tailed distribution when the market is going down. The main source of asymmetric scaling behavior in the Shanghai stock market are long-range correlations, whereas that in the Shenzhen stock market is fat-tailed distribution. An analysis of the time-varying feature of scaling asymmetries shows that the evolution trends of these scaling asymmetries are similar in the two Chinese stock markets. Major financial and economical events may enhance scaling asymmetries.     

Observation of long-range compositional fluctuations in glasses: implications for atomic and electronic structure

Experimental evidence for long-range compositional fluctuations in glasses is given. The implications for electronic structure and stoichiometry-induced structural variations are analyzed. These fluctuations were discovered by examining the spatial dependence of inner shell near-edge absorption spectra obtained using a 50nm diameter probe. This spectroscopy is sensitive to both angular and distance correlations in bonding. Comparisons with spectra from compositionally equivalent crystals, and multiple-scattering calculations which include core-hole effects are used to analyze the data.     

Long-range spatial correlations in the exciton energy distribution in GaAs/AlGaAs quantum wells

Variations in the width of a quantum well (QW) are known to be a source of broadening of the exciton line. Using low temperature near-field optical microscopy, we have exploited the dependence of exciton energy on well width to show that in GaAs QWs, these seemingly random well-width fluctuations actually exhibit well-defined order-strong long-range correlations appearing laterally, in the plane of the QW, as well as vertically, between QWs grown one on top of the other. We show that these fluctuations are correlated with the commonly found mound structure on the surface. This is an intrinsic property of molecular beam epitaxial growth.     

Fluctuations and long-range order in finite-temperature pion condensates

We study the stability of the neutral and charged pion-condensed phases of nuclear matter against fluctuations of the order parameter. At finite temperatures pion condensates with an order parameter varying in only one dimension are, as we show, prohibited, while such condensates are allowed at zero temperature. Condensates that vary in two and three dimensions can be stable at all temperatures. Another allowed state, which may be favored energetically, is a quasi-ordered one-dimensional condensate characterized by long-range pion field correlations decaying only algebraically in space; insufficient experimental resolution may, however, limit one's ability to distinguish such a one-dimensional structure from true one-dimensional long-range order. Finally, we calculate the normal modes and the pion propagator in a charged one-dimensional running-wave condensate, explicitly illustrating the effect of long-range Coulomb forces on the order-parameter fluctuations.     

Fluctuations and correlations in the string clustering approach

The fluctuations due to the clustering of color sources can explain the behaviour of the scaled multiplicity variance and transverse momentum fluctuations with centrality. They also predict a nonmonotonic behaviour with centrality for the multiplicity associated to high-p_T events. The clustering of color sources gives rise to an increase in the long-range correlations with centrality as well as to a supression at high centrality with respect to superposition models.     

Multifractal properties of Chinese stock market in Shanghai

In this article, we apply three methods of multifractal analysis, partition function method, singular spectrum method and multifractal detrended fluctuation analysis method, to analyze the closing index fluctuations of Shanghai stock market during the past seven years. We have found that Shanghai stock market has weak multifractal features and there are long-range power-law correlations between index series. The shapes of singular spectrums do not change with time scales and their strengths weaken when the scales shorten. But when the orders of partition function increase, the strengths of multifractal increase, the singular spectrums become rougher and the general Hurst exponents decrease. These results provide solid and important values for further study on the dynamic mechanism of stock market price fluctuation.     

Multifractal detrended fluctuation analysis of the Chinese stock index futures market

Based on the multifractal detrended fluctuation analysis (MF-DFA) and multifractal spectrum analysis, this paper empirically studies the multifractal properties of the Chinese stock index futures market. Using a total of 2942 ten-minute closing prices, we find that the Chinese stock index futures returns exhibit long-range correlations and multifractality, making the single-scale index insufficient to describe the futures price fluctuations. Further, by comparing the original time series with the transformed time series through shuffling procedure and phase randomization procedure, we show the existence of two different sources of the multifractality for the Chinese stock index futures market. Our results suggest that the multifractality is mainly due to long-range correlations, although the fat-tailed probability distributions also contribute to such multifractal behaviour.     

Fractal landscapes in biological systems: long-range correlations in DNA and interbeat heart intervals

Here we discuss recent advances in applying ideas of fractals and disordered systems to two topics of biological interest, both topics having common the appearance of scale-free phenomena, i.e., correlations that have no characteristic length scale, typically exhibited by physical systems near a critical point and dynamical systems far from equilibrium. (i) DNA nucleotide sequences have traditionally been analyzed using models which incorporate the possibility of short-range nucleotide correlations. We found, instead, a remarkably long-range power law correlation. We found such long-range correlations in intron-containing genes and in non-transcribed regulatory DNA sequences as well as intragenomic DNA, but not in cDNA sequences or intron-less genes. We also found that the myosin heavy chain family gene evolution increases the fractal complexity of the DNA landscapes, consistent with the intron-late hypothesis of gene evolution. (ii) The healthy heartbeat is traditionally thought to be regulated according to the classical principle of homeostasis, whereby physiologic systems operate to reduce variability and achieve an equilibrium-like state. We found, however, that under normal conditions, beat-to-beat fluctuations in heart rate display long-range power law correlations.     

Long-range correlations of the polarized-light intensity in disordered samples

The spatial correlation function of intensity fluctuations in a speckle formed by polarized light multiply scattered in a disordered sample has been calculated. The dependence of the long-range spatial correlations on the polarization state of incident light and the depolarizing properties of the medium has been determined for the cases of transmission and reflection.     

Transport in random correlated fields

A review is given of recent developments in the diffusion properties of particles in the presence of local random fields as well as the conductivity of the analog random resistor network. The effect of long-range ferro- and antiferro-type correlations between the local fields on the diffusion and conductivity properties is considered. A physical realization for such spatial correlations is diffusion on linear polymers in the presence of external uniform bias field. For this case a universal diffusion law was found independent of the fractal dimension of the polymer chain or the Euclidean dimension in which the polymer is embedded. Recent results for diffusion in two dimensions in the presence of a special case of correlated local fields are also reviewed.