Related papers: Average Spread Complexity and the Higher-Order Lev…
We study a quantum particle propagating through a ``quantum mechanically chaotic'' background, described by parametric random matrices with only short range spatial correlations. The particle is found to exhibit turbulent-like diffusion…
A nonuniform system is considered consisting of two phases with different densities of particles. At each given time the distribution of the phases in space is chaotic: each phase filling a set of regions with random shapes and locations. A…
Disordered systems are an important class of models in statistical mechanics, having the defining characteristic that the energy landscape is a fixed realization of a random field. Examples include various models of glasses and polymers.…
In a recent work \cite{LiuJoladSchZia13}, we introduced dynamic networks with preferred degrees and presented simulation and analytic studies of a single, homogeneous system as well as two interacting networks. Here, we extend these studies…
We consider the statistics of the results of a measurement of the spreading operator in the Krylov basis generated by the Hamiltonian of a quantum system starting from a specified initial pure state. We first obtain the probability…
A new class of probabilistic models for cascading failure propagation in interconnected systems is proposed. The models take into account important characteristics of real systems that are not considered in existing generic approaches.…
We show that the characteristic function of the probability distribution associated with the change of an observable in a two-point measurement protocol with a perturbation can be written as an auto-correlation function between an initial…
Quantum complexity is a measure of the minimal number of elementary operations required to approximately prepare a given state or unitary channel. Recently, this concept has found applications beyond quantum computing -- in studying the…
Due to the regularization effect of the stochastic noise, the quantitative entropy-cost type propagation of chaos for mean field interacting particle system is proposed. The result shows that the Kac's chaotic property measured in relative…
Molecular dynamics simulations with varying damping are used to examine the effects of inertia and spatial dimension on sheared disordered solids in the athermal, quasistatic limit. In all cases the distribution of avalanche sizes follows a…
The explicit analytical expression for the distribution function of parametric derivatives of energy levels ("level velocities") with respect to a random change of scattering potential is derived for the chaotic quantum systems belonging to…
When the complete understanding of a complex system is not available, as, e.g., for systems considered in the real-world, we need a top-down approach to complexity. In this approach one may start with the desire to understand general…
Complexity is an interdisciplinary concept which, first of all, addresses the question of how order emerges out of randomness. For many reasons matrices provide a very practical and powerful tool in approaching and quantifying the related…
The scaling property of level statistics in the quantum Hall regime, i.e. 2D disordered electron systems subject to strong magnetic fields, is analyzed numerically in the light of the random matrix theory. The energy dependences of the…
We use series expansions to study dynamics of equilibrium and non-equilibrium systems on networks. This analytical method enables us to include detailed non-universal effects of the network structure. We show that even low order…
Collective behavior is studied in globally coupled maps with distributed nonlinearity. It is shown that the heterogeneity enhances regularity in the collective dynamics. Low-dimensional quasiperiodic motion is often found for the…
A large class of technically non-chaotic systems, involving scatterings of light particles by flat surfaces with sharp boundaries, is nonetheless characterized by complex random looking motion in phase space. For these systems one may…
A central task in analyzing complex dynamics is to determine the loci of information storage and the communication topology of information flows within a system. Over the last decade and a half, diagnostics for the latter have come to be…
In the context of epidemic spreading, many intricate dynamical patterns can emerge due to the cooperation of different types of pathogens or the interaction between the disease spread and other failure propagation mechanism. To unravel such…
Random Threshold Networks with sparse, asymmetric connections show complex dynamical behavior similar to Random Boolean Networks, with a transition from ordered to chaotic dynamics at a critical average connectivity $K_c$. In this type of…