Fractal-Type Dynamical Behaviors of Complex Systems (original) (raw)

Comments on Chaotic and Fractal Behavior in Atoms and Molecules

Progress of Theoretical Physics Supplement, 1994

We introduce a classification scheme for atomic and molecular systems that have been studied as problems of "quantum chaos" according to the particle number and the degrees of freedom involved in the system. This is followed by discussion of various approaches to the study of classical-quantum correspondence of driven systems. § 1. Introduction

Fractals, Multifractals, and Thermodynamics

Zeitschrift für Naturforschung A, 1988

The basic concept of fractals and multifractals are introduced for pedagogical purposes, and the present status is reviewed. The emphasis is put on illustrative examples with simple mathematical structures rather than on numerical methods or experimental techniques. As a general characteriza­tion of fractals and multifractals a thermodynamical formalism is introduced, establishing a connec­tion between fractal properties and the statistical mechanics of spin chains.

Fractal Structure in Ionization Dynamics

Few-Body Systems, 2006

Critical stability of few-body quantum systems was held at the Max-Planck Institute for the Physics of Complex Systems in Dresden from October 16 to 22, 2005. As for the previous workshops, at Trento in 1997, and Les Houches in 2001, the main motivation was to discuss questions that are shared by specialists of different fields, and are formulated, tentatively solved and further developed using slightly different methods and languages. This interdisciplinary character, ranging from mathematical physics to quantum chemistry, via molecular, atomic, nuclear and hadron physics, was an essential ingredient of these workshops, and linked with the foundation of few-body physics. The present meeting increased slightly the emphasis on atomic and molecular physics and also on mathematical-statistical physics in the area of condensed matter. The following subjects were proposed in the call for abstracts and invitations: 1. Weakly Coulomb or gravitational-bound few-body states. 2. Weakly short-range-interaction bound few-body states. 3. Continuum structure and few-body decay properties. 4. Dynamical few-body problems near instability. 5. Correlation in boson-fermion and mixed condensates 6. Few-body correlation within many-body systems. 7. Exotic structures: Efimov, tango, Borromean and halo states. 8. Lower-dimensional systems. 9. Semi-classical methods.

Overview of electrical processes in fractal geometry: from electrodynamic relaxation to superconductivity

Proceedings of The IEEE, 1993

This paper is devoted to a general analysis of the consequences of the parametrization of the fractal set on the electrodynamics of this set. The relevance of scaling properties to electrochemical, dielectric, and magnetic relaxations is considered with a special emphasis on the use of noninteger derivative operators in electromagnetism and superconductivity. In electromagnetism, the above analysis gives a brief overview of the main results already obtained, focusing especially on the introduction of dissipative terms in the equation of propagation and on the generalized form of the uncertainty principle in fractal media. The new Laplacian and d'dlembertian operators are evoked as well as the scale relativity on which this new analysis is founded. For superconductivity, the analysis introduces a geometrical interpretation founded on frustration acting not only on topology but on the metric of the space-time in a particular type of fractal geometry. Although this point of view may appear as a breakthrough in the theory of superconductors, the model offers some relations with the theory of fractional statistics and the theory of Anyons. force at the interface is given by: @ = k . A p where k is a constant [l], [2], 4 is the nonstationary part of the flow, A p is the thermodynamic driving force of the process. The nonstationary part of the flow of charge injection into the surrounding J is obviously proportional to the product of 1500

arXiv:physics/0601009v3 [physics.ed-ph] 14 Oct 2013

In this manuscript various components of research are listed and briefly discussed. The topics considered in this write-up cover a part of the research methodology paper of Master of Philosophy (M.Phil.) course and Doctor of Philosophy (Ph.D.) course. The manuscript is intended for students and research scholars of science subjects such as mathematics, physics, chemistry, statistics, biology and computer science. Various stages of research are discussed in detail. Special care has been taken to motivate the young researchers to take up challenging problems. Ten assignment works are given. For the benefit of young researchers a short interview with three eminent scientists is included at the end of the manuscript. * Electronic address: rajasekar@cnld.bdu.ac.in