A Physical Explanation of Quasiperiodic Motion and the Onset of Chaos in Nonlinear Systems

Abstract

The reader may have noticed that the subject broadly called classical and quantum nonlinear dynamics has lately gained considerable attention in many fields of physics and chemistry [1–4]. Of particular interest is the dynamics of systems of many oscillators coupled by nonlinear interactions. Such systems are used to model widely spread phenomena, for example, molecular vibrations, intra-molecular energy transfer, unimolecular reaction, and laser-matter interactions. In the latter case, the laser is viewed, using the classical idea of extended phase space, or quantum field theory, as an oscillator. Hence, multiphoton excitations of atomic, molecular and plasma systems are described using oscillators coupled in a nonlinear manner. In a completely different area we find the motion of galaxies is also modeled by nonlinear oscillators [5]. Recently the physics of light traveling in fibers (fiber optics) has been shown to obey similar equations. Atomic and molecular physics is far from left out. The nature of electronic excited states (e.g. doubly excited Rydberg states) and the whole question of the ability to assign quantum numbers to states and to corresponding spectra involves nonlinear ideas. The unusual behavior of electronic states in strong external fields is essentially governed by nonlinear equations.