Turbulence hierarchy in foreign exchange markets.

We present a multiscale stochastic analysis of foreign exchange rates using the H-theory formalism, which provides a hierarchical intermittency model for the information cascade in the currency market. We examine the distributions of returns and volatilities for the three most traded currency pairs: euro-U.S.

Turbulence Hierarchy and Multifractality in the Integer Quantum Hall Transition.

We offer a new perspective on the problem of characterizing mesoscopic fluctuations in the interplateau regions of the integer quantum Hall transition. We found that longitudinal and transverse conductance fluctuations, generated by varying the external magnetic field within a microscopic model, are multifractal and lead to distributions of conductance increments (magnetoconductance) with heavy tails (intermittency) and signatures of a hierarchical structure (cascade) in the corresponding stochastic process, akin to Kolmogorov's theory of fluid turbulence. We confirm this picture by interpreting the stochastic process of the conductance increments in the framework of H theory, which is a continuous-time stochastic approach that incorporates the basic features of Kolmogorov's theory.

Simultaneous evaluation of intermittency effects, replica symmetry breaking and modes dynamics correlations in a Nd:YAG random laser.

Random lasers (RLs) are remarkable experimental platforms to advance the understanding of complex systems phenomena, such as the replica-symmetry-breaking (RSB) spin glass phase, dynamics modes correlations, and turbulence. Here we study these three phenomena jointly in a Nd:YAG based RL synthesized for the first time using a spray pyrolysis method. We propose a couple of modified Pearson correlation coefficients that are simultaneously sensitive to the emergence and fading out of photonic intermittency turbulent-like effects, dynamics evolution of modes correlations, and onset of RSB behavior.

Evaluation of Pearson correlation coefficient and Parisi parameter of replica symmetry breaking in a hybrid electronically addressable random fiber laser.

The hybrid electronically addressable random (HEAR) laser is a novel type of random fiber laser that presents the remarkable property of selection of the fiber section with lasing emission. Here we present a joint analysis of the correlations between intensity fluctuations at distinct wavelengths and replica symmetry breaking (RSB) behavior of the HEAR laser. We introduce a modified Pearson coefficient that simultaneously comprises both the Parisi overlap parameter and standard Pearson correlation coefficient.

Evidence of a Floquet Phase in a Photonic System.

The ground breaking extension of the key concept of phase structure to nonequilibrium regimes was only recently achieved in Floquet systems, characterized by a time-dependent quantum Hamiltonian with a periodic driving source. However, despite the theoretical advances, only very few systems are known to display experimental Floquet phases, not one of them employing a laser emission-based mechanism. Here we report the first experimental observation of a Floquet phase in a photonic system, a disordered fiber laser with spatial eigenmode localization.

Coexistence of turbulence-like and glassy behaviours in a photonic system.

Coexistence of physical phenomena can occur in quite unexpected ways. Here we demonstrate the first evidence in any physical system of the coexistence in the same set of measurements of two of the most challenging phenomena in complex systems: turbulence and spin glasses. We employ a quasi-one-dimensional random fibre laser, which displays all essential ingredients underlying both behaviours, namely disorder, frustration and nonlinearity, as well as turbulent energy cascades and intermittent energy flux between fluctuation scales.

Turbulence hierarchy in a random fibre laser.

Turbulence is a challenging feature common to a wide range of complex phenomena. Random fibre lasers are a special class of lasers in which the feedback arises from multiple scattering in a one-dimensional disordered cavity-less medium. Here we report on statistical signatures of turbulence in the distribution of intensity fluctuations in a continuous-wave-pumped erbium-based random fibre laser, with random Bragg grating scatterers.

Universality classes of fluctuation dynamics in hierarchical complex systems.

A unified approach is proposed to describe the statistics of the short-time dynamics of multiscale complex systems. The probability density function of the relevant time series (signal) is represented as a statistical superposition of a large time-scale distribution weighted by the distribution of certain internal variables that characterize the slowly changing background. The dynamics of the background is formulated as a hierarchical stochastic model whose form is derived from simple physical constraints, which in turn restrict the dynamics to only two possible classes.