In this paper, we modify Laskars simplified model of planetary evolution and accretion [J. Laskar, Phys. Rev. Lett, vol 84, p 3240 (2000)] to account for the full conservation of the total angular momentum of the system, and extend it to incorporate
an accretion probability that depends on the mass and relative velocity of the colliding particles. We present statistical results for the mass and eccentricity of the planets formed, in terms of their semi-major axes, for a large number of realisations of differe
The phase--space volume of regions of regular or trapped motion, for bounded or scattering systems with two degrees of freedom respectively, displays universal properties. In particular, sudden reductions in the phase-space volume or gaps are observe
d at specific values of the parameter which tunes the dynamics; these locations are approximated by the stability resonances. The latter are defined by a resonant condition on the stability exponents of a central linearly stable periodic orbit. We show that, for more than two degrees of freedom, these resonances can be excited opening up gaps, which effectively separate and reduce the regions of trapped motion in phase space. Using the scattering approach to narrow rings and a billiard system as example, we demonstrate that this mechanism yields rings with two or more components. Arcs are also obtained, specifically when an additional (mean-motion) resonance condition is met. We obtain a complete representation of the phase-space volume occupied by the regions of trapped motion.
A characteristic feature of thermalized non-equilibrated matter is that, in spite of energy relaxation (thermalization), a phase memory of the way the strongly interacting many-body system was excited remains. In this contribution we analyze a low en
ergy evaporating proton data in nucleon induced reactions at $simeq$62 MeV incident energy with $^{197}$Au, $^{208}$Pb, $^{209}$Bi and $^{nat}$U. Our analysis demonstrates that the thermalized non-equilibrated matter survives a cascade of several evaporating particles. Thus the experiments show that the effect of the anomalously slow phase relaxation, with upper limits of the phase relaxation widths in the range 1-10$^{-4}$ eV, is stable with respect to the multi-step evaporating cascade from the thermalized compound nuclei. We also briefly mention manifestations and implications of the thermalized non-equilibrated matter for some other fields.
A characteristic feature of thermalized non-equilibrated matter is that, in spite of energy relaxation--equilibration, a phase memory of the way the many-body system was excited remains. As an example, we analyze data on a strong forward peaking of t
hermal proton yield in the Bi($gamma$,p) photonuclear reaction. New analysis shows that the phase relaxation in highly-excited heavy nuclei can be 8 orders of magnitude or even much longer than the energy relaxation. We argue that thermalized non-equilibrated matter resembles a high temperature superconducting state in quantum many-body systems. We briefly present results on the time-dependent correlation function of the many-particle density fluctuations for such a superconducting state. It should be of interest to experimentally search for manifestations of thermalized non-equilibrated matter in many-body mesoscopic systems and nanostructures.
