Small violations of full correlation Bell inequalities for multipartite pure random states

We estimate the probability of random $N$-qudit pure states violating full-correlation Bell inequalities with two dichotomic observables per site. These inequalities can show violations that grow exponentially with $N$, but we prove this is not the typical case. For many-qubit states the probability to violate any of these inequalities by an amount that grows linearly with $N$ is vanishingly small. If each system's Hilbert space dimension is larger than two, on the other hand, the probability of seeing \emph{any} violation is already small. For the qubits case we discuss furthermore the consequences of this result for the probability of seeing arbitrary violations (\emph i.e., of any order of magnitude) when experimental imperfections are considered.Comment: 16 pages, one colum

Power-law random walks

We present some new results about the distribution of a random walk whose independent steps follow a $q-$Gaussian distribution with exponent $\frac{1}{1-q}; q \in \mathbb{R}$. In the case $q>1$ we show that a stochastic representation of the point reached after $n$ steps of the walk can be expressed explicitly for all $n$. In the case $q<1,$ we show that the random walk can be interpreted as a projection of an isotropic random walk, i.e. a random walk with fixed length steps and uniformly distributed directions.Comment: 5 pages, 4 figure

Tails of probability density for sums of random independent variables

The exact expression for the probability density $p_{_N}(x)$ for sums of a finite number $N$ of random independent terms is obtained. It is shown that the very tail of $p_{_N}(x)$ has a Gaussian form if and only if all the random terms are distributed according to the Gauss Law. In all other cases the tail for $p_{_N}(x)$ differs from the Gaussian. If the variances of random terms diverge the non-Gaussian tail is related to a Levy distribution for $p_{_N}(x)$. However, the tail is not Gaussian even if the variances are finite. In the latter case $p_{_N}(x)$ has two different asymptotics. At small and moderate values of $x$ the distribution is Gaussian. At large $x$ the non-Gaussian tail arises. The crossover between the two asymptotics occurs at $x$ proportional to $N$. For this reason the non-Gaussian tail exists at finite $N$ only. In the limit $N$ tends to infinity the origin of the tail is shifted to infinity, i. e., the tail vanishes. Depending on the particular type of the distribution of the random terms the non-Gaussian tail may decay either slower than the Gaussian, or faster than it. A number of particular examples is discussed in detail.Comment: 6 pages, 4 figure

First passage time for subdiffusion: The nonextensive entropy approach versus the fractional model

We study the similarities and differences between different models concerning subdiffusion. More particularly, we calculate first passage time (FPT) distributions for subdiffusion, derived from Greens' functions of nonlinear equations obtained from Sharma-Mittal's, Tsallis's and Gauss's nonadditive entropies. Then we compare these with FPT distributions calculated from a fractional model using a subdiffusion equation with a fractional time derivative. All of Greens' functions give us exactly the same standard relation $=2 D_\alpha t^\alpha$ which characterizes subdiffusion ($0<\alpha<1$), but generally FPT's are not equivalent to one another. We will show here that the FPT distribution for the fractional model is asymptotically equal to the Sharma--Mittal model over the long time limit only if in the latter case one of the three parameters describing Sharma--Mittal entropy $r$ depends on $\alpha$, and satisfies the specific equation derived in this paper, whereas the other two models mentioned above give different FTPs with the fractional model. Greens' functions obtained from the Sharma-Mittal and fractional models - for $r$ obtained from this particular equation - are very similar to each other. We will also discuss the interpretation of subdiffusion models based on nonadditive entropies and the possibilities of experimental measurement of subdiffusion models parameters.Comment: 12 pages, 8 figure

Soil aggregation under different management systems

Considering that the soil aggregation reflects the interaction of chemical, physical and biological soil factors, the aim of this study was evaluate alterations in aggregation, in an Oxisol under no-tillage (NT) and conventional tillage (CT), since over 20 years, using as reference a native forest soil in natural state. After analysis of the soil profile (cultural profile) in areas under forest management, samples were collected from the layers 0-5, 5-10, 10-20 and 20-40 cm, with six repetitions. These samples were analyzed for the aggregate stability index (ASI), mean weighted diameter (MWD), mean geometric diameter (MGD) in the classes > 8, 8-4, 4-2, 2-1, 1-0.5, 0.5-0.25, and < 0.25 mm, and for physical properties (soil texture, water dispersible clay (WDC), flocculation index (FI) and bulk density (Bd)) and chemical properties (total organic carbon - COT, total nitrogen - N, exchangeable calcium - Ca2+, and pH). The results indicated that more intense soil preparation (M < NT < PC) resulted in a decrease in soil stability, confirmed by all stability indicators analyzed: MWD, MGD, ASI, aggregate class distribution, WDC and FI, indicating the validity of these indicators in aggregation analyses of the studied soil

Brownian motion of a charged particle driven internally by correlated noise

We give an exact solution to the generalized Langevin equation of motion of a charged Brownian particle in a uniform magnetic field that is driven internally by an exponentially-correlated stochastic force. A strong dissipation regime is described in which the ensemble-averaged fluctuations of the velocity exhibit transient oscillations that arise from memory effects. Also, we calculate generalized diffusion coefficients describing the transport of these particles and briefly discuss how they are affected by the magnetic field strength and correlation time. Our asymptotic results are extended to the general case of internal driving by correlated Gaussian stochastic forces with finite autocorrelation times.Comment: 10 pages, 4 figures with subfigures, RevTeX, v2: revise

Edgeworth Expansion of the Largest Eigenvalue Distribution Function of GUE Revisited

We derive expansions of the resolvent Rn(x;y;t)=(Qn(x;t)Pn(y;t)-Qn(y;t)Pn(x;t))/(x-y) of the Hermite kernel Kn at the edge of the spectrum of the finite n Gaussian Unitary Ensemble (GUEn) and the finite n expansion of Qn(x;t) and Pn(x;t). Using these large n expansions, we give another proof of the derivation of an Edgeworth type theorem for the largest eigenvalue distribution function of GUEn. We conclude with a brief discussion on the derivation of the probability distribution function of the corresponding largest eigenvalue in the Gaussian Orthogonal Ensemble (GOEn) and Gaussian Symplectic Ensembles (GSEn)

The ensemble of random Markov matrices

The ensemble of random Markov matrices is introduced as a set of Markov or stochastic matrices with the maximal Shannon entropy. The statistical properties of the stationary distribution pi, the average entropy growth rate $h$ and the second largest eigenvalue nu across the ensemble are studied. It is shown and heuristically proven that the entropy growth-rate and second largest eigenvalue of Markov matrices scale in average with dimension of matrices d as h ~ log(O(d)) and nu ~ d^(-1/2), respectively, yielding the asymptotic relation h tau_c ~ 1/2 between entropy h and correlation decay time tau_c = -1/log|nu| . Additionally, the correlation between h and and tau_c is analysed and is decreasing with increasing dimension d.Comment: 12 pages, 6 figur

Stationary states in Langevin dynamics under asymmetric L\'evy noises

Properties of systems driven by white non-Gaussian noises can be very different from these systems driven by the white Gaussian noise. We investigate stationary probability densities for systems driven by $\alpha$-stable L\'evy type noises, which provide natural extension to the Gaussian noise having however a new property mainly a possibility of being asymmetric. Stationary probability densities are examined for a particle moving in parabolic, quartic and in generic double well potential models subjected to the action of $\alpha$-stable noises. Relevant solutions are constructed by methods of stochastic dynamics. In situations where analytical results are known they are compared with numerical results. Furthermore, the problem of estimation of the parameters of stationary densities is investigated.Comment: 9 pages, 9 figures, 3 table

Sign-time distribution for a random walker with a drifting boundary

We present a derivation of the exact sign-time distribution for a random walker in the presence of a boundary moving with constant velocity.Comment: 5 page