Nonextensive Statistical Mechanics

254 7 Thermodynamical and Nonthermodynamical Applications7.1.9.2 El NiñoThe Southern Oscillation Index (SOI) corresponds to the daily registration of theoceanic temperature (including appropriate pressure corrections) at a fixed point ofthe Earth. Histograms can be constructed by using values separated by a fixed timelag. They are well fitted by q-Gaussians with q depending on the time lag [292,293].See Figs. 7.43 and 7.44. Like for financial returns, the index q gradually approachesunity (i.e., Gaussian distribution) when the time lag increases, which correspondsof course to an increasing loss of time correlation of the successive values of thesignal. A micro- or meso-scopic theory interprets the results exhibited in Figs. 7.43and 7.44 would of course be welcome.Further geophysical applications, e.g., to clouds [294], the Stromboli volcano[295], geological faults [295], are available in the literature as well.7.1.10 Quantum ChaosThe quantum kicked top (QKT) is a paradigmatic system showing quantum chaos.In its regular regime, the overlap function O behaves roughly constant with time,and, in the strongly chaotic regime, it decreases exponentially with time before theemergence of quantum interference effects. It is therefore possible that, precisely inthe frontier between both regions, the exponential time dependence of the overlap1.25fit in Fig.2Eq.(13)q1.21.15K r/K L10 0.2Eq.(11)Eq.(12)10 0.1 Δt/Δt L1.1δ = 0.111.0510 0 10 –3 10 –2 10 –1 10 0Δt L= 48 monthsSOI; Jan 1866 − Jan 2006110 −3 10 −2 10 −110 0Δt /Δt LFig. 7.43 Dependence of q on the (conveniently rescaled) time lag for the SOI. The data correspondto the Jan 1866–Jan 2006 period. See [292] for further details.