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We derive a criterion for the onset of chaos in systems consisting of two massive, eccentric, coplanar planets. Given the planets masses and separation, the criterion predicts the critical eccentricity above which chaos is triggered. Chaos occurs where mean motion resonances overlap, as in Wisdom (1980)s pioneering work. But whereas Wisdom considered only nearly circular planets, and hence examined only first order resonances, we extend his results to arbitrarily eccentric planets (up to crossing orbits) by examining resonances of all orders. We thereby arrive at a simple expression for the critical eccentricity. We do this first for a test particle in the presence of a planet, and then generalize to the case of two massive planets, based on a new approximation to the Hamiltonian (Hadden, in prep). We then confirm our results with detailed numerical simulations. Finally, we explore the extent to which chaotic two-planet systems eventually result in planetary collisions.
We derive a semi-analytic criterion for the presence of chaos in compact, eccentric multiplanet systems. Beyond a minimum semimajor-axis separation, below which the dynamics are chaotic at all eccentricities, we show that (i) the onset of chaos is de
A simple metric can be used to determine whether a planet or exoplanet can clear its orbital zone during a characteristic time scale, such as the lifetime of the host star on the main sequence. This criterion requires only estimates of star mass, pla
When, in the course of searching for exoplanets, sparse sampling and noisy data make it necessary to disentangle possible solutions to the observations, one must consider the possibility that what appears to be a single eccentric Keplerian signal may
We prove a necessary and sufficient condition for the occurrence of entanglement in two two-level systems, simple enough to be of experimental interest. Our results are illustrated in the context of a spin star system analyzing the exact entanglement evolution of the central couple of spins.
We show that the onset of quantum chaos at infinite temperature in two many-body 1D lattice models, the perturbed spin-1/2 XXZ and Anderson models, is characterized by universal behavior. Specifically, we show that the onset of quantum chaos is marke