Related papers: Symbol-to-symbol correlation function at the Feige…
We demonstrate that the dynamics towards and within the Feigenbaum attractor combine to form a q-deformed statistical-mechanical construction. The rate at which ensemble trajectories converge to the attractor (and to the repellor) is…
Orbital-free density functional theory promises to deliver linear-scaling electronic structure calculations. This requires the knowledge of the non-interacting kinetic-energy density functional (KEDF), which should be accurate and must…
A multi-time extension of a density correlation function is introduced to reveal temporal information about dynamical heterogeneity in glass-forming liquids. We utilize a multi-time correlation function that is analogous to the higher-order…
The relationship between period doubling bifurcations and Feigenbaum's constants has been studied for nearly 40 years and this relationship has helped uncover many fundamental aspects of universal scaling across multiple nonlinear dynamical…
A new method of symbolic analysis based on finite discretization of velocity-curvature space is proposed. A minimum alphabet is introduced in a natural way, and a number of initial analytic measures are defined that make it possible to…
A theory of systems with long-range correlations based on the consideration of binary N-step Markov chains is developed. In the model, the conditional probability that the i-th symbol in the chain equals zero (or unity) is a linear function…
The slow dynamics for a colloidal suspension of particles interacting with a hard-core repulsion complemented by a short-ranged attraction is discussed within the frame of mode-coupling theory for ideal glass transitions for parameter…
A fast simulation algorithm for the calculation of multitime correlation functions of open quantum systems is presented. It is demonstrated that any stochastic process which ``unravels'' the quantum Master equation can be used for the…
A statistical mechanics argument relating partition functions to martingales is used to get a condition under which random geometric processes can describe interfaces in 2d statistical mechanics at criticality. Requiring multiple SLEs to…
In this article, we develop a functional-analytic framework to establish existence, uniqueness, regularity of disintegration, and statistical properties of equilibrium states for a broad class of dynamical systems, potentially discontinuous…
It is shown that fractional derivatives of the (integrated) invariant measure of the Feigenbaum map at the onset of chaos have power-law tails in their cumulative distributions, whose exponents can be related to the spectrum of…
Cold atom systems provide a rich platform to realize strongly interacting condensed matter systems, and recent progress in fluorescence imaging technique has enabled identification of nontrivial doublon, singlon, and holon correlation…
Symbolic dynamics, which partitions an infinite number of finite-length trajectories into a finite number of trajectory sets, describes the dynamics of a system in a simplified and coarse-grained way with a limited number of symbols. The…
Symbolizations, the base of symbolic dynamic analysis, are classified as global static and local dynamic approaches which are combined by joint entropy in our works for nonlinear dynamic complexity analysis. Two global static methods,…
Initially, the logistic map became popular as a simplified model for population growth. In spite of its apparent simplicity, as the population growth-rate is increased the map exhibits a broad range of dynamics, which include bifurcation…
We use symbolic dynamics to study discrete-time dynamical systems with multiple time delays. We exploit the concept of avoiding sets, which arise from specific non-generating partitions of the phase space and restrict the occurrence of…
We consider the dynamical behavior of Martin-L\"of random points in dynamical systems over metric spaces with a computable dynamics and a computable invariant measure. We use computable partitions to define a sort of effective symbolic…
Visibility algorithms are a family of geometric and ordering criteria by which a real-valued time series of N data is mapped into a graph of N nodes. This graph has been shown to often inherit in its topology non-trivial properties of the…
Recent results on particle momentum and spin correlations are discussed in view of the role played by the effects of quantum statistics, including multiboson and coherence phenomena, and final state interaction. Particularly, it is…
Bifurcations in a system of coupled maps are investigated. Using symbolic dynamics it is proven that for coupled shift maps the well known space--time--mixing attractor becomes unstable at a critical coupling strength in favour of a…