Production of trans-Neptunian binaries through chaos-assisted capture

The recent discovery of binary objects in the Kuiper-belt opens an invaluable window into past and present conditions in the trans-Neptunian part of the Solar System. For example, knowledge of how these objects formed can be used to impose constraints on planetary formation theories. We have recently proposed a binary-object formation model based on the notion of chaos-assisted capture. Here we present a more detailed analysis with calculations performed in the spatial (three-dimensional) three- and four-body Hill approximations. It is assumed that the potential binary partners are initially following heliocentric Keplerian orbits and that their relative motion becomes perturbed as these objects undergo close encounters. First, the mass, velocity, and orbital element distribu- tions which favour binary formation are identified in the circular and elliptical Hill limits. We then consider intruder scattering in the circular Hill four-body problem and find that the chaos-assisted capture mechanism is consistent with observed, apparently randomly distributed, binary mutual orbit inclinations. It also predicts asymmetric distributions of retrograde versus prograde orbits. The time-delay induced by chaos on particle transport through the Hill sphere is analogous to the formation of a resonance in a chemical reaction. Implications for binary formation rates are considered and the 'fine-tuning' problem recently identified by Noll et al. (2007) is also addressed.Comment: submitted to MNRA

Capture and escape in the elliptic restricted three-body problem

Several families of irregular moons orbit the giant planets. These moons are thought to have been captured into planetocentric orbits after straying into a region in which the planet's gravitation dominates solar perturbations (the Hill sphere). This mechanism requires a source of dissipation, such as gas-drag, in order to make capture permanent. However, capture by gas-drag requires that particles remain inside the Hill sphere long enough for dissipation to be effective. Recently we have proposed that in the circular restricted three-body problem particles may become caught up in `sticky' chaotic layers which tends to prolong their sojourn within the planet's Hill sphere thereby assisting capture. Here we show that this mechanism survives perturbations due to the ellipticity of the planet's orbit. However, Monte Carlo simulations indicate that the planet's ability to capture moons decreases with increasing orbital eccentricity. At the actual Jupiter's orbital eccentricity, this effects in approximately an order of magnitude lower capture probability than estimated in the circular model. Eccentricities of planetary orbits in the Solar System are moderate but this is not necessarily the case for extrasolar planets which typically have rather eccentric orbits. Therefore, our findings suggest that these extrasolar planets are unlikely to have substantial populations of irregular moons.Comment: This is a preprint of an Article accepted for publication in Monthly Notices of the Royal Astronomical Society, (C) 2004 The Royal Astronomical Societ

Statistical Theory of Asteroid Escape Rates

Transition states in phase space are identified and shown to regulate the rate of escape of asteroids temporarily captured in circumplanetary orbits. The transition states, similar to those occurring in chemical reaction dynamics, are then used to develop a statistical semianalytical theory for the rate of escape of asteroids temporarily captured by Mars. Theory and numerical simulations are found to agree to better than 1%. These calculations suggest that further development of transition state theory in celestial mechanics, as an alternative to large-scale numerical simulations, will be a fruitful approach to mass transport calculations

Do Higher Cigarette Prices Encourage Youth to Use Marijuana?

Every major national tobacco legislation proposed in the past two years has called for significant increases in the price of cigarettes as a way to discourage youths from smoking. One argument used to oppose these bills is that increases in the price of cigarettes would cause youths to substitute marijuana for cigarettes. Although it has long been believed that cigarettes are a gateway drug,' no economic research has been done to determine whether cigarettes and marijuana are economic complements or substitutes. This paper begins to fill the void in the current research by examining the contemporaneous relationship between the demands for cigarettes and marijuana among a nationally representative sample of 8th, 10th and 12th graders from the 1992-1994 Monitoring the Future Project. Two part models are used to estimate reduced form demand equations. Examination of the cross-price effects clearly shows that higher cigarette prices will not increase marijuana use among youths. In addition to reducing youth smoking, we find that higher cigarette prices significantly reduce the average level of marijuana used by current users. Cigarette prices also have a negative effect on the probability of using marijuana findings are not significant at conventional levels.

Solution of the two identical ion Penning trap final state

We have derived a closed form analytic expression for the asymptotic motion of a pair of identical ions in a high precision Penning trap. The analytic solution includes the effects of special relativity and the Coulomb interaction between the ions. The existence and physical relevance of such a final state is supported by a confluence of theoretical, experimental and numerical evidence.Comment: 5 pages and 2 figure

Fractal Weyl law behavior in an open, chaotic Hamiltonian system

We numerically show fractal Weyl law behavior in an open Hamiltonian system that is described by a smooth potential and which supports numerous above-barrier resonances. This behavior holds even relatively far away from the classical limit. The complex resonance wave functions are found to be localized on the fractal classical repeller.Comment: 4 pages, 3 figures. to appear in Phys Rev

Spontaneous emission of non-dispersive Rydberg wave packets

Non dispersive electronic Rydberg wave packets may be created in atoms illuminated by a microwave field of circular polarization. We discuss the spontaneous emission from such states and show that the elastic incoherent component (occuring at the frequency of the driving field) dominates the spectrum in the semiclassical limit, contrary to earlier predictions. We calculate the frequencies of single photon emissions and the associated rates in the "harmonic approximation", i.e. when the wave packet has approximately a Gaussian shape. The results agree well with exact quantum mechanical calculations, which validates the analytical approach.Comment: 14 pages, 4 figure

Squeezing of electromagnetic field in a cavity by electrons in Trojan states

The notion of the Trojan state of a Rydberg electron, introduced by I.Bialynicki-Birula, M.Kali\'nski, and J.H.Eberly (Phys. Rev. Lett. 73, 1777 (1994)) is extended to the case of the electromagnetic field quantized in acavity. The shape of the electronic wave packet describing the Trojan state is practically the same as in the previously studied externally driven system. The fluctuations of the quantized electromagnetic field around its classical value exhibit strong squeezing. The emergence of Trojan states in the cylindrically symmetrical system is attributed to spontaneous symmetry braking.Comment: 9 pages, 8 figure