Related papers: A Structure behind Primitive Chaos
We introduce the notion of domain-structured chaos and apply it to establish a connection between stochastic dynamics and deterministic chaos.
A source of unpredictability is equivalent to a source of information: unpredictability means not knowing which of a set of alternatives is the actual one; determining the actual alternative yields information. The degree of…
Chaotic systems which are due to nonlinearity have attracted a great concern in the current world and chaotic models. Systems for a wide range of operation conditions have their application in almost all branches of engineering and science.…
The basic laws of physics are simple, so why is the world complex? The theory of self-organized criticality posits that complex behavior in nature emerges from the dynamics of extended, dissipative systems that evolve through a sequence of…
Classical chaos is marked by an extreme sensitivity to initial conditions, where infinitesimally close trajectories separate exponentially over time. In quantum mechanics, however, unitary evolution and the uncertainty principle preclude…
We introduce an analytical solution to the one of the most familiar problems from the elementary quantum mechanics textbooks. The following discussion provides simple illustrations to a number of general concepts of quantum chaology, along…
The universal dynamic uncertainty, discovered in Parts I and II of this series of papers for the case of Hamiltonian quantum systems, is further specified to reveal the hierarchical structure of levels of dynamically redundant…
We propose a formalism which defines chaos in both quantum and classical systems in an equivalent manner by means of \textit{adiabatic transformations}. The complexity of adiabatic transformations which preserve classical time-averaged…
One of the basic concepts of modern physics with a long prehistory is a fluid, which means a substance that flows under an applied shear stress. In this sense fluids form a wide subset of the phases of matter that includes liquids, dense…
Fuzziness and randomicity widespread exist in natural science, engineering, technology and social science. The purpose of this paper is to present a new logic - uncertain propositional logic which can deal with both fuzziness by taking…
A simple experiment using radioactive decay is proposed to test the possibility of a determinsistic, but chaotic, origin of quantum mechanical randomness.
This paper is a personal overview of the efforts over the last half century to understand fluid turbulence in terms of simpler coherent units. The consequences of chaos and the concept of coherence are first reviewed, using examples from…
Nonlinear dynamics (``chaos theory'') and quantum mechanics are two of the scientific triumphs of the 20th century. The former lies at the heart of the modern interdisciplinary approach to science, whereas the latter has revolutionized…
According to quantum theory, randomness is a fundamental property of the universe yet classical physics is mostly deterministic. In this article I show that it is possible for deterministic systems to arise from random ones and discuss the…
We examine whether the chaotic behavior of classical systems with a limited number of degrees of freedom can produce quantum dephasing, against the conventional idea that dephasing takes place only in large systems with a huge number of…
A relativistic cosmological perturbation theory for the Friedmann-Lema\^itre-Robertson-Walker universe is presented that explains the masses and formation times of the first structures in our universe. First, it is shown that, without a…
A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene…
The representations of the world around in physics built with help of causality are analyzed and seems incomplete. The observer's causal representations form a closed logical system, i.e. the compact group related to cause-effect chains.…
Chaos associated with bifurcation makes a new science, but the origin and essence of chaos are not yet clear. Based on the well-known logistic map, chaos used to be regarded as intrinsic randomicity of determinate dynamics systems. However,…
While classical chaos is defined via a system's sensitive dependence on its initial conditions (SDIC), this notion does not directly extend to quantum systems. Instead, recent works have established defining both quantum and classical chaos…