Macroscopic behavior in a simple chaotic Hamiltonian system

Abstract

Nonlinear Hamiltonian systems of only two degrees of freedom readily produce complicated Poincare-type (or, synonymously, chaotic) behavior. Nonlinear Hamiltonian systems of many degrees of freedom, on the other hand, produce not only chaos, but also modulate systematic motions (so-called dissipative structures). A two-degrees-of-freedom system is described which shows two types of ‘macroscopic’ behavior: On one hand, there is a ‘main regime’ which is characterized by a random distribution of both positional variables. From this ‘equilibrium’ the system only very rarely departs once it has come close to it. On the other hand, when the system is started sufficiently far away, it spends a certain time in a characteristic ‘transient regime’ which too (like the main regime) is the same for both time directions. One of the two particles hereby shows a statistical directional preference. This preference is the same as when the system is run as an open system (‘temporarily open regime’). The simple nature of the system encourages further quantitative and qualitative investigations.