Related papers: Integrability and chaos: the classical uncertainty
Classical chaos arises from the inherent non-linearity of dynamical systems. However, quantum maps are linear; therefore, the definition of chaos is not straightforward. To address this, we study a quantum system that exhibits chaotic…
In this article one introduces a formalism of classical mechanics where complex Lagrangian functions are admitted. The results include complex versions of the Lagrangian function, of the Euler-Lagrange equation, of the Hamilton principle, a…
General relativity exhibits a unique feature not represented in standard examples of chaotic systems; it is a spacetime diffeomorphism invariant theory. Thus many characterizations of chaos do not work. It is therefore necessary to develop…
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 study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. - This is motivated by the ``timeless''…
This paper proposes a basic theory on physical reality and a new foundation for quantum mechanics and classical mechanics. It presents a scenario not only to solve the problem of the arbitrariness on the operator ordering for the…
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…
Classical physics is generally regarded as deterministic, as opposed to quantum mechanics that is considered the first theory to have introduced genuine indeterminism into physics. We challenge this view by arguing that the alleged…
This paper summarises a numerical investigation of how the usual manifestations of chaos and regularity for flows in time-independent Hamiltonians can be alterred by a systematic time-dependence of the form arising naturally in an expanding…
Stable chaos is a generalization of the chaotic behaviour exhibited by cellular automata to continuous-variable systems and it owes its name to an underlying irregular and yet linearly stable dynamics. In this review we discuss analogies…
Over the preceeding twenty years, the role of underlying classical dynamics in quantum mechanical tunneling has received considerable attention. A number of new tunneling phenomena have been uncovered that have been directly linked to the…
How classical chaos emerges from the underlying quantum world is a fundamental problem in physics. The origin of this question is in the correspondence principle. Classical chaos arises due to non-linear dynamics, whereas quantum mechanics,…
In previous study [1], we proposed a new physical law applicable to both particle and thermodynamical systems. Additionally, we introduced a physical definition of chaos and self-organization. In the present work, we extend this novel…
We address the issue of the quantum-classical correspondence in chaotic systems using, as recently done by Zurek [e-print quant-ph/9802054], the solar system as a whole as a case study: this author shows that the classicality of the…
Quasi-integrable Hamiltonian systems are of great interest in many research fields of physics and mathematics. In these systems, the phase space has regular and chaotic trajectories. These trajectories depend in part on the magnitude of…
A widely accepted definition of ``quantum chaos'' is ``the behavior of a quantum system whose \emph{classical} \emph{limit is chaotic}''. The dynamics of quantum-chaotic systems is nevertheless very different from that of their classical…
We describe some highlights in the theory of chaos, that started with Poincare (1899). Generic systems have both ordered and chaotic domains. Chaos appears mainly near un- stable periodic orbits. Large chaotic domains are due to resonance…
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…
In quantum systems with a classical limit, advanced semiclassical methods provide the crucial link between phase-space structures, reflecting the distinction between chaotic, mixed or integrable classical dynamics, and the corresponding…
The behaviour of an electron in a potential that resembles that of a bidimensional solid with a perpendicular magnetic field applied is studied from a classical point of view. This problem presents the standard features of chaos and some…