CHAOS AND FRACTALS IN NANO AND QUANTUM TECHNOLOGY

The talk will first give a brief general introduction to modern nonlin ear dynamics which will encompass Chaos and Fractals before moving on to discuss the impact of these new concepts and tools on engineering, quantum physics and political sciences. Basic concepts such as stabili ty, bifurcation and sensitive dependence on initial conditions will be explained. The interrelationship between chaos and fractals will be o utlined using a simple real experiment and its computer simulation. Th is experiment is essentially a simplified three-body problem with a fr actal basin of attraction where the sensitivity to initial conditions is due to Canter-like sets at the boundary of three adjacent fields of attraction. We start with foundational problems then go on to applica tions in electronic and quantum devices using state of the art laser a nd nanotechnology. In particular we discuss the relation between Canto rian spacetime, the geometry of the four manifold and fake R-4 as well as squeezed quantum states. In conclusion some experiments are outlin ed which are intended to show that micro spacetime must be a Cantorian -fractal geometrical construct and that the path of a quantum particle possesses a mean fractal Hausdorff dimension < d(H)> = 2. The urgency of establishing a Center of excellence for advanced quantum technolog y in Egypt for the Middle East in which all Arab countries (at least) should participate, will be emphasized with regard to the crucial econ omic development in the region. A colour 20 minute video film on Chaos and Fractals in a simple Poincare nonintegrable system will be shown. (C) 1998 Elsevier Science Ltd. All rights reserved.