Brain neurons as quantum computers: {\it in vivo} support of background physics

The question: whether quantum coherent states can sustain decoherence, heating and dissipation over time scales comparable to the dynamical timescales of the brain neurons, is actively discussed in the last years. Positive answer on this question is crucial, in particular, for consideration of brain neurons as quantum computers. This discussion was mainly based on theoretical arguments. In present paper nonlinear statistical properties of the Ventral Tegmental Area (VTA) of genetically depressive limbic brain are studied {\it in vivo} on the Flinders Sensitive Line of rats (FSL). VTA plays a key role in generation of pleasure and in development of psychological drug addiction. We found that the FSL VTA (dopaminergic) neuron signals exhibit multifractal properties for interspike frequencies on the scales where healthy VTA dopaminergic neurons exhibit bursting activity. For high moments the observed multifractal (generalized dimensions) spectrum coincides with the generalized dimensions spectrum calculated for a spectral measure of a {\it quantum} system (so-called kicked Harper model, actively used as a model of quantum chaos). This observation can be considered as a first experimental ({\it in vivo}) indication in the favour of the quantum (at least partially) nature of the brain neurons activity

Chaos from turbulence: stochastic-chaotic equilibrium in turbulent convection at high Rayleigh numbers

It is shown that correlation function of the mean wind velocity generated by a turbulent thermal convection (Rayleigh number $Ra \sim 10^{11}$) exhibits exponential decay with a very long correlation time, while corresponding largest Lyapunov exponent is certainly positive. These results together with the reconstructed phase portrait indicate presence of chaotic component in the examined mean wind. Telegraph approximation is also used to study relative contribution of the chaotic and stochastic components to the mean wind fluctuations and an equilibrium between these components has been studied in detail

Components of multifractality in high-frequency stock returns

We analyzed multifractal properties of 5-minute stock returns from a period of over two years for 100 highly capitalized American companies. The two sources: fat-tailed probability distributions and nonlinear temporal correlations, vitally contribute to the observed multifractal dynamics of the returns. For majority of the companies the temporal correlations constitute a much more significant related factor, however.Comment: to appear in Physica

Fluctuations of temperature gradients in turbulent thermal convection

Broad theoretical arguments are proposed to show, formally, that the magnitude G of the temperature gradients in turbulent thermal convection at high Rayleigh numbers obeys the same advection-diffusion equation that governs the temperature fluctuation T, except that the velocity field in the new equation is substantially smoothed. This smoothed field leads to a -1 scaling of the spectrum of G in the same range of scales for which the spectral exponent of T lies between -7/5 and -5/3. This result is confirmed by measurements in a confined container with cryogenic helium gas as the working fluid for Rayleigh number Ra=1.5x10^{11}. Also confirmed is the logarithmic form of the autocorrelation function of G. The anomalous scaling of dissipation-like quantities of T and G are identical in the inertial range, showing that the analogy between the two fields is quite deep

Multiscaling of galactic cosmic ray flux

Multiscaling analysis of differential flux dissipation rate of galactic cosmic rays (Carbon nuclei) is performed in the energy ranges: 56.3-73.4 Mev/nucleon and 183.1-198.7 MeV/nucleon, using the data collected by ACE/CRIS spacecraft instrument for 2000 year. The analysis reveals strong (turbulence-like) intermittency of the flux dissipation rate for the short-term intervals: 1-30 hours. It is also found that type of the intermittency can be different in different energy ranges

Critical Fluctuation of Wind Reversals in Convective Turbulence

The irregular reversals of wind direction in convective turbulence are found to have fluctuating intervals that can be related to critical behavior. It is shown that the net magnetization of a 2D Ising lattice of finite size fluctuates in the same way. Detrended fluctuation analysis of the wind reversal time series results in a scaling behavior that agrees with that of the Ising problem. The properties found suggest that the wind reversal phenomenon exhibits signs of self-organized criticality.Comment: 4 RevTeX pages + 3 figures in ep

Multifractality in the stock market: price increments versus waiting times

By applying the multifractal detrended fluctuation analysis to the high-frequency tick-by-tick data from Deutsche B\"orse both in the price and in the time domains, we investigate multifractal properties of the time series of logarithmic price increments and inter-trade intervals of time. We show that both quantities reveal multiscaling and that this result holds across different stocks. The origin of the multifractal character of the corresponding dynamics is, among others, the long-range correlations in price increments and in inter-trade time intervals as well as the non-Gaussian distributions of the fluctuations. Since the transaction-to-transaction price increments do not strongly depend on or are almost independent of the inter-trade waiting times, both can be sources of the observed multifractal behaviour of the fixed-delay returns and volatility. The results presented also allow one to evaluate the applicability of the Multifractal Model of Asset Returns in the case of tick-by-tick data.Comment: Physica A, in prin

Directed Fixed Energy Sandpile Model

We numerically study the directed version of the fixed energy sandpile. On a closed square lattice, the dynamical evolution of a fixed density of sand grains is studied. The activity of the system shows a continuous phase transition around a critical density. While the deterministic version has the set of nontrivial exponents, the stochastic model is characterized by mean field like exponents.Comment: 5 pages, 6 figures, to be published in Phys. Rev.

Intermittency and the passive nature of the magnitude of the magnetic field

It is shown that the statistical properties of the magnitude of the magnetic field in turbulent electrically conducting media resemble, in the inertial range, those of passive scalars in fully developed three-dimensional fluid turbulence. This conclusion, suggested by the data from Advanced Composition Explorer, is supported by a brief analysis of the appropriate magnetohydrodynamic equations

Beyond scaling and locality in turbulence

An analytic perturbation theory is suggested in order to find finite-size corrections to the scaling power laws. In the frame of this theory it is shown that the first order finite-size correction to the scaling power laws has following form $S(r) \cong cr^{\alpha_0}[\ln(r/\eta)]^{\alpha_1}$, where $\eta$ is a finite-size scale (in particular for turbulence, it can be the Kolmogorov dissipation scale). Using data of laboratory experiments and numerical simulations it is shown shown that a degenerate case with $\alpha_0 =0$ can describe turbulence statistics in the near-dissipation range $r > \eta$, where the ordinary (power-law) scaling does not apply. For moderate Reynolds numbers the degenerate scaling range covers almost the entire range of scales of velocity structure functions (the log-corrections apply to finite Reynolds number). Interplay between local and non-local regimes has been considered as a possible hydrodynamic mechanism providing the basis for the degenerate scaling of structure functions and extended self-similarity. These results have been also expanded on passive scalar mixing in turbulence. Overlapping phenomenon between local and non-local regimes and a relation between position of maximum of the generalized energy input rate and the actual crossover scale between these regimes are briefly discussed.Comment: extended versio