ORDER, CHAOS AND NUCLEAR-DYNAMICS

The relation between the order-to-chaos transition in the dynamics of independent classical particles in a container, and the transition from an elastic to a dissipative response of the container to shape changes, is studied by means of computer simulations. The validity of the wall formula for energy dissipation is confirmed in the case of containers whose surfaces are rippled according to Legendre polynomials P3, P4, P5, P6, in which case the particle trajectories are largely chaotic, as revealed by Poincare sections in phase space. The opposite limit of an elastic response is illustrated by means of spheroidal containers of various eccentricities, for which the particle trajectories are integrable and the phase space is foliated by tori. Fission-like deformations are also considered, for which the response of the container changes from elastic to dissipative with increasing deformation. Idealized giant-dipole oscillations of the gas are studied for spherical as well as deformed containers. A generalization of the wall formula valid for long times (i.e., for arbitrarily large excitations of the gas) is constructed. The principal lesson of these studies is that a gas of independent particles in a time-dependent container does not behave at all like a gas.