Many-body chaos near a thermal phase transition

We study many-body chaos in a (2+1)D relativistic scalar field theory at high temperatures in the classical statistical approximation, which captures the quantum critical regime and the thermal phase transition from an ordered to a disordered phase. We evaluate out-of-time ordered correlation functions (OTOCs) and find that the associated Lyapunov exponent increases linearly with temperature in the quantum critical regime, and approaches the non-interacting limit algebraically in terms of a fluctuation parameter. OTOCs spread ballistically in all regimes, also at the thermal phase transition, where the butterfly velocity is maximal. Our work contributes to the understanding of the relation between quantum and classical many-body chaos and our method can be applied to other field theories dominated by classical modes at long wavelengths.

Entropy of Measurements of Electric and Non-eleCtric Systems Fluctuating Parameters

Fluctuations of the measured parameters of the investigated electric and non-electric systems are considered on the thermodynamics basis. We have defined that entropy of the investigated system in relation to environment depends on the correlation between measuring duration Тmeas of the system’s fluctuation parameter and the system’s relaxation time τ. Decrement of the energy spectrum of fluctuations with the decrease of frequency is explained by Тmeas > τ. When Тmeas ≈ Nmaxτ (where Nmax is the number of possible ways to create the balanced state of the system), entropy of investigated system tends to zero in relation to the environment, and the measurement error caused by fluctuations becomes the minimal.

Recombination line abundances in NGC 6210

We present abundances derived from echelle spectroscopy of the planetary nebula NGC 6210 from the forbidden, collisionally excited lines, and from the permitted, recombination lines. We have obtained spectra from 3 positions in the nebula: at the central star, and 6 and 12 arcseconds south of the central star. We find a discrepancy of a factor of 2 between the O2+/H+ ratio derived by the recombination lines and by the forbidden lines in each spatial position. This discrepancy may result from the presence of temperature fluctuations in NGC 6210, where the collisionally excited lines are exponentially weighted to regions of higher temperature. A value for the root-mean-square temperature fluctuation parameter t2(OIIabun)= 0.038+0.007–0.009 is derived for the central star spectrum, 0.040+0.006–0.013 for the 6 arcsecond offset, and 0.051+0.014–0.015 for the 12 arcsecond offset spectrum. Thus no significant variation in t2 is seen as a function of spatial position within the nebula. We have also estimated t2 by comparing the derived Balmer Jump temperature at the 6 arcsecond offset, Te(BaJ)= 7900+2400–1600K, with the temperature derived from the [O III] 5007/4363å ratio Te[O III]= 9370±100K at this position. This comparison suggest t2(BaJ)= 0.041±0.020, in agreement with the values for t2 as estimated from the recombination lines.

Effect of Aortic Arch Atherosclerotic Formations on Blood Mass Flow Distribution

The effect of the aortic arch atherosclerotic formations on blood mass flow distribution is determined experimentally on the aortic arch model, derived from x-ray traces, for the average values of the governing parameters: Reynolds number, unsteadiness parameter, and velocity fluctuation parameter. A computer program incorporating the experimrntal data is developed, which predicts approximately the flow distribution for various arterial blockages.