Strongly correlated variables and existence of a universal distribution function for relative fluctuations

If two random values plotted against each other form a curve close to a straight line, these values are defined as strongly correlated with each other. In this paper, we define these two random values as satisfying the linear principle for strongly correlated variables (LPSCV). For variables of such kind, it is possible to find a new and very general class of distribution functions. One can show that detrended random sequences for relative fluctuations presented in the form of the sequences of ranged amplitudes (SRAs) satisfy the LPSCV. The first results of such kind, based on the analysis of the SRAs, confirm the fact that many random sequences are strongly correlated. For detrended sequences (obtained by numerical differentiation), characterized by a large sampling volume (N > 1000), the found distribution function, describing the SRA envelopes, can be written as [1] F(t) = a ₁ t ^v ₁ + a ₂ t ^v ₂. The results obtained in this study open new possibilities for analysis of many complex systems, where the natural relationships are very difficult to find and in cases where they are not known. Examples based on available data confirm this basic statement and show that the envelopes of relative fluctuations presented in the form of SRAs are described by the general distribution function found here.     

Single-particle distribution function of a quantum dot system at finite temperature

In the present paper, we shall rigorously re-establish the result of the single-particle function of a quantum dot system at finite temperature. Unlike the proof given in our previous work (Phys. Rev. B 74 195414 (2006)), we take a different approach, which does not exploit the explicit expression of the Gibbs distribution function. Instead, we only assume that the statistical distribution function of the quantum dot system is thermodynamically stable. As a result, we are able to show clearly that the electronic structure in the quantum dot system is completely determined by its thermodynamic stability. Furthermore, the weaker requirements on the statistical distribution function also make it possible to apply the same method to the quantum dot systems in non-equilibrium states.     

Single-particle distribution function of a quantum dot system at finite temperature

In the present paper,we shall rigorously re-establish the result of the single-particle function of a quantum dot system at finite temperature.Unlike the proof given in our previous work(Phys.Rev.B 74 195414(2006)),we take a different approach,which does not exploit the explicit expression of the Gibbs distribution function.Instead,we only assume that the statistical distribution function of the quantum dot system is thermodynamically stable.As a result,we are able to show clearly that the electronic structure in the quantum dot system is completely determined by its thermodynamic stability.Furthermore,the weaker requirements on the statistical distribution function also make it possible to apply the same method to the quantum dot systems in non-equilibrium states.     

Superstatistics and temperature fluctuations

Superstatistics [Beck and Cohen (2003) [1]] is a formalism aimed at describing statistical properties of a generic extensive quantity E in complex out-of-equilibrium systems in terms of a linear superposition of equilibrium canonical distributions. The weight function $P(\beta )$ is argued to be provided by the statistics of the intensive thermodynamic quantity β conjugate to E [Beck (2011) [14]], and therefore is expected to be determined by the spatiotemporal dynamics alone of the system under consideration. In this paper, recalling a previous work [Beck (2006) [21]], I show by examples that, in some cases fulfilling all the conditions for the superstatistics formalism to be applicable, $P(\beta )$ cannot be defined uniquely, but rather depends upon the way the measurement of E is performed.     

Steady state probability distribution for turbulence fluctuations

An incompressible and viscous fluid is represented by a complex scalar field. In terms of, the hydrodynamic mode interaction v. grad v can be described canonically, i.e. as a functional derivative of a Hamiltonian. By introducing noise and stochastic damping a Langevin equation and its corresponding Fokker-Planck equation is obtained. Both are expected to describe a turbulent flow. The stochastic process approximately obeys detailed balance. This allows to derive, as a main result, the stationary distribution function of a turbulent fluid. It is non Gaussian, contains a 4^th order (transverse) current-current interaction, and has mass (~ ²) zero.     

Sound amplitude fluctuations due to a temperature microstructure

The experiments reported in this paper were carried out in a water tank in which a random medium was generated by convective mixing from an array of heaters. An approximate thermodynamic model of the medium was derived. Temperature measurements were made which showed that the temperature microstructure created in this way could be considered as a passive additive of turbulence. Furthermore, it was possible to characterize the random refractive index in terms of a spectral distribution by using an adapted version of a spectrum proposed by Medwin for the upper ocean. By using the adapted Medwin model and the single-scatter theoretical results of Tatarski, theoretical estimates were obtained of the fluctuations of an acoustic signal propagating in this particular medium. Experiments were carried out to measure acoustic signal amplitude fluctuations at frequencies of 9 MHz and 1 MHz. The empirical results were in agreement with the theoretical estimates. Measurements are also reported for the spatial correlation functions of the acoustic signal amplitude fluctuations. The results are discussed in the light of currently available theoretical results.     

Spontaneous fluctuations of a temperature filament in a magnetized plasma

This experiment illustrates the spatiotemporal pattern of the fluctuations that spontaneously develop in a magnetized temperature filament whose transverse scale is comparable to the electron skin depth. A high-frequency mode exhibits a striking spiral structure and is identified as a drift-Alfven eigenmode. A low-frequency mode is found to be localized near the center of the filament. It is documented that the fluctuations significantly increase the transport of heat beyond the prediction of classical theory based on Coulomb collisions.     

Analysis of daily temperature fluctuations

We study daily temperature fluctuations over more than 50 yr in two places on the globe that are separated by more than 3000 km. We analyze the temperature fluctuations ΔT_i with respect to the mean noon temperature 〈T_i〉 averaged, for each day of the year, over the whole year, ΔT_i = T_i − 〈T_i〉. We find that the ΔT_i are correlated and can be characterized for up to at least 10³ days by a power law correlation with an exponent α ≅ 0.65.     

Statistical model for a quantum noiseless subsystem

One of the most promising physical properties for implementing quantum technology is light polarization. However, since light polarization is fragile, it is crucial to use quantum error correction in order to make quantum information over optical networks feasible. This paper performs a statistical analysis of a noiseless subsystem technique to correct errors on quantum information sent through light polarization. We discuss the performance of the noiseless subsystem scheme in a noisy channel using a two-dimensional random walk to represent the channel variation. Finally, we propose an expression to measure the efficiency of the analyzed setup using the degree of depolarization of the light.     

Vortex structures and temperature fluctuations in a bluff-body burner

Vortical and thermal structures of non-premixed propane flame in a bluff-body burner are studied experimentally in the transition from laminar to turbulent flow. In particular, we focus attention on the effect of annular air flow on the flame. The small-scale inner vortices inside the flame is stimulated by the annular air flow, and outside the flame, small eddies due to turbulence rather than the large-scale outer vortices due to thermal buoyancy become dominant with increasing air velocity. The interrelation between the vortical and thermal structures is analyzed by looking at the frequency spectrum and probability density function of temperature fluctuations.     

The projection-like techniques for Wigner's distribution function

Starting from the quantum Liouville equation for many-particle distribution function an evolution equation for fully factorized and symmetrized Wigner's distribution function is derived. Our approach is formally similar to the projection operator method. Details of the used techniques are presented as an example of the two-particle system.A greater part of the presented paper was realized under the auspices of the late Professor A. Pawikowski. The author wants to dedicate this paper to his memory. He would also like to thank Dr. J. uczka for critical reading of the first version of this paper and valuable advice.     

Clipped time autocorrelation function of intensity fluctuations for a non gaussian field

Numerical results for the single and double clipped autocorrelation functions of intensity fluctuations of squared intensity of gaussian-exponential field are reported and compared with the unclipped ones.     

Method for measuring the electron distribution function in the low temperature plasma with a high time resolution

A hybrid method for measuring the electron distribution function in the low temperature plasma is described. The time resolution of the measurement is of the order of several sec.     

The Wigner distribution function

In this letter, the relationship between the characteristic function for two arbitrary noncommuting observables and a generalized Wigner distribution function is established. This distribution function is shown to have no simple interpretation in the sense of probability theory but, in lieu of its special properties, can be used directly for calculating the expectation values of observables.     

The twist elastic constant as a function of temperature for nematic MBBA

The quantity K_twist/X_anisotropy has been measured as a function of temperature. The results show, that near the clearing temperature this quantity is not proportional to the long range order parameter.     

The effects of fluctuations and nonuniformities on line-reversal temperature measurements

An analysis of line-reversal temperature measurements in the presence of fluctuations and nonuniformities is presented. The theory provides a method for the measurement of mean temperatures and temperature fluctuation intensities in certain combustion flows. Experiments with controlled and random fluctuations are interpreted by means of the analysis.     

Density correlations induced by temperature fluctuations in a photon gas

The impact of angular temperature variations on the thermodynamic variables and real-space correlation functions of black-body radiation are analyzed. In particular, the effect of temperature fluctuations on the number density and energy density correlations of the cosmic microwave background (CMB) is studied. The angular temperature fluctuations are modeled by an isotropic and homogeneous Gaussian random field, whose autocorrelation function is defined on the unit sphere in momentum space. This temperature correlation function admits an angular Fourier transform which determines the density correlations in real space induced by temperature fluctuations. In the case of the CMB radiation, the multipole coefficients of the angular power spectrum defining the temperature correlation function have been measured by the Planck satellite. The fluctuation-induced perturbation of the equilibrium variables (internal energy, entropy, heat capacity and compressibility) can be quantified in terms of the measured multipole coefficients by expanding the partition function around the equilibrium state in powers of the temperature random field. The real-space density correlations can also be extracted from the measured temperature power spectrum. Both the number density and energy density correlations of the electromagnetic field are long-range, admitting power-law decay; in the case of the energy density correlation, the fluctuation-induced correlation overpowers the isotropic equilibrium correlation in the long-distance limit.     

Generalization of the theory of thermophoresis for a doublet of solid particles experiencing a temperature step on the surface

Using the linear operator approach, a theory of thermophoresis is constructed for the case of two homogenous solid spherical aerosol particles moving parallel to their center line. Formulas for the Stokes force, force of thermophoresis, and rate of thermophoresis of an aerosol particle with regard to a temperature step on its surface and the effect of the other particle are derived. Approximate engineering formulas are presented.