Geometric structures, fractal self-similarity, squeezed coherent states and electrodynamics

Abstract

The formalism describing fractal self-similar structures has been shown in recent works to be isomorphic to the one of a system of damped/amplified oscillators, which is a prototype of a dissipative system and of the environment in which it is embedded, and to squeezed coherent states. Fractal-like structures appear to be generated by coherent quantum condensation processes, and thus they appear as macroscopic quantum systems, as it happens with crystals, ferromagnets, superconductors and like systems characterized by ordered patterns. In this report, by resorting to such results it is shown that in space-time regions where the magnetic field may be approximated to be constant and the electric field is derivable from a harmonic potential, the isomorphism also exists between electrodynamics and fractal-like structures. A link is thus established between self-similarity, dissipation, coherent states and electrodynamics. The relation between quantum dissipation and non-commutative geometry in the plane is also commented upon. The macroscopic appearances (forms) of the fractals seem to emerge out of a process of morphogenesis as the macroscopic manifestation of the underlying dissipative, coherent quantum dynamics.