Based on 1-min price changes recorded since year 2012, the fluctuation properties of the rapidly emerging Bitcoin market are assessed over chosen sub-periods, in terms of return distributions, volatility autocorrelation, Hurst exponents, and multiscaling effects. The findings are compared to the stylized facts of mature world markets. While early trading was affected by system-specific irregularities, it is found that over the months preceding April 2018 all these statistical indicators approach the features hallmarking maturity. This can be taken as an indication that the Bitcoin market, and possibly other cryptocurrencies, carry concrete potential of imminently becoming a regular market, alternative to the foreign exchange. Since high-frequency price data are available since the beginning of trading, the Bitcoin offers a unique window into the statistical characteristics of a market maturation trajectory.
Multifractal detrended cross-correlation methodology is described and applied to Foreign exchange (Forex) market time series. Fluctuations of high-frequency exchange rates of eight major world currencies over 2010-2018 period are used to study cross-correlations. The study is motivated by fundamental questions in complex systems' response to significant environmental changes and by potential applications in investment strategies, including detecting triangular arbitrage opportunities. Dominant multiscale cross-correlations between the exchange rates are found to typically occur at smaller fluctuation levels. However, hierarchical organization of ties expressed in terms of dendrograms, with a novel application of the
The ionization of hydrogen Rydberg atoms by circularly polarized microwaves is studied quantum mechanically in a model two-dimensional atom. We apply a combination of a transformation to the coordinate frame rotating with the field, with complex rotation approach and representation of the atomic subspace in a Sturmian-type basis. The diagonalization of resulting matrices allows us to treat exactly the ionization of atoms initially prepared in highly excited Rydberg states of principal quantum number n 0 Ϸ60. Similarities and differences between ionization by circularly and linearly polarized microwaves are discussed with a particular emphasis on the high-frequency regime and on the localization phenomenon. The dependence of the ionization character on the initial state ͑circular, elliptical, or low angular momentum state͒ as well as on the helicity of the polarization is discussed in detail. It is shown that, in the high-frequency chaotic regime, close encounters with the nucleus do not play a major role in the ionization process.
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