Biomedical subjects
Publications and source records attributed to R. H. Parmenter.
The system consisting of three identical harmonic oscillators impulsively coupled can be described by the four-dimensional triple-twist map. This map is capable of generating a uniform stochastic web, periodic in all four dimensions. Some properties of this web are studied.
Quantum mechanical equations of motion are obtained for a system consisting of a very large number of three types of interacting bosons. Under suitable choice of parameters of the Hamiltonian of the system, the equations of motion are those describing three Josephson junctions in a superconducting loop. It is shown numerically that this system is capable of exhibiting deterministic chaos (extreme sensitivity to initial conditions).
Evidence is given that many classes of periodically kicked Hamiltonian system with 1.5 degree of freedom generate infinite, uniform stochastic webs. The kick term in the Hamiltonian or the equation of motion need not be purely sinusoidal or some small perturbation of a sinusoidal function. For the resonance condition q=4 the structure of the web can be different from a square lattice; However, remarkably symmetric patterns of chaos are still present throughout the whole phase space. Examples are given for the square wave function and sawtooth function in the kick term of the equation of motion. The sensitive dependence on initial conditions of those systems is investigated.
It is shown that the same kind of deterministic chaos that occurs in classical systems can occur in certain quantum mechanical, many-body systems. The example of the physical realization of the periodically kicked quantum spin (PKQS) is considered in detail. The quantum mechanical equations of motion for this system can be converted into the three-dimensional PKQS map, which exhibits deterministic chaos and Arnold diffusion. Although the case of quantum spin s= 1/2 is assumed, it is shown that the same map results for s=1 (but not for s>/=3/2), and for a suitably chosen classical particle with orbital angular momentum. A simple generalization of the PKQS model gives rise to stochastic webs on the surface of the unit sphere very similar to the Zaslavsky stochastic webs in a plane.