Complexity in Nonlinear and Quantum Optics by Considering Kolmogorov Derivatives and Change Complexity Information Measures

Abstract

One of the most challenging tasks in studying phenomena in nonlinear and quantum optics is determining the contributions of the complexities of individual components to the complexity of the entire system (master complexity). To examine these contributions, we considered this issue using information measures: Kolmogorov derivatives based on Kolmogorov complexity (KC) [KC spectrum, KC plane], change complexity (CC), and Lyapunov exponent (λ). We applied these measures to daily time series measured from 2003 to 2005 in Novi Sad (Serbia) for ultraviolet (UV) radiation, which represents a physical complex system, and water vapor pressure as individual components of that system. Based on the measures applied to UV radiation, we determined: (i) the level of chaos and randomness of the measured time series; (ii) the coordinates of points in the KC plane where master and individual amplitudes interact; and (iii) the range of UV radiation amplitudes in which changes in the interaction between the master and individual amplitudes are most pronounced.