Secular Evolution of Hierarchical Planetary Systems

(Abridged) We investigate the dynamical evolution of coplanar hierarchical two-planet systems where the ratio of the orbital semimajor axes alpha=a_1/a_2 is small. The orbital parameters obtained from a multiple Kepler fit to the radial velocity variations of a star are best interpreted as Jacobi coordinates and Jacobi coordinates should be used in any analyses of hierarchical planetary systems. An approximate theory that can be applied to coplanar hierarchical two-planet systems with a wide range of masses m_j and orbital eccentricities e_j is the octupole-level secular perturbation theory (OSPT). The OSPT shows that if the ratio of the maximum orbital angular momenta, lambda \approx (m_1/m_2) alpha^{1/2}, for given a_j is approximately equal to a critical value lambda_{crit}, then libration of the difference in the longitudes of periapse, w_1-w_2, about either 0 or 180 deg. is almost certain, with possibly large amplitude variations of both e_j. We establish that the OSPT is highly accurate for systems with alpha<0.1 and reasonably accurate even for systems with alpha as large as 1/3, provided that alpha is not too close to a significant mean-motion commensurability or above the stability boundary. The HD 168443 system is not in a secular resonance and its w_1-w_2 circulates. The HD 12661 system is the first extrasolar planetary system found to have w_1-w_2 librating about 180 deg. The libration of w_1-w_2 and the large-amplitude variations of both e_j in the HD 12661 system are consistent with the analytic results on systems with lambda \approx lambda_{crit}. The HD 12661 system with the best- fit orbital parameters and sin i = 1 is affected by the close proximity to the 11:2 commensurability, but small changes in the outer orbital period can result in configurations that are not affected by mean-motion commensurabilities.Comment: 32 pages, including 8 figures; uses AASTeX v5.0; accepted for publication in Ap

A Primordial Origin of the Laplace Relation Among the Galilean Satellites

Understanding the origin of the orbital resonances of the Galilean satellites of Jupiter will constrain the longevity of the extensive volcanism on Io, may explain a liquid ocean on Europa, and may guide studies of the dissipative properties of stars and Jupiter-like planets. The differential migration of the newly formed Galilean satellites due to interactions with a circumjovian disk can lead to the primordial formation of the Laplace relation n_1 - 3 n_2 + 2 n_3 = 0, where the n_i are the mean orbital angular velocities of Io, Europa, and Ganymede, respectively. This contrasts with the formation of the resonances by differential expansion of the orbits from tidal torques from Jupiter.Comment: 13 pages, including 4 figures; uses scicite.st

Sample-specific and Ensemble-averaged Magnetoconductance of Individual Single-Wall Carbon Nanotubes

We discuss magnetotransport measurements on individual single-wall carbon nanotubes with low contact resistance, performed as a function of temperature and gate voltage. We find that the application of a magnetic field perpendicular to the tube axis results in a large magnetoconductance of the order of e^2/h at low temperature. We demonstrate that this magnetoconductance consists of a sample-specific and of an ensemble-averaged contribution, both of which decrease with increasing temperature. The observed behavior resembles very closely the behavior of more conventional multi-channel mesoscopic wires, exhibiting universal conductance fluctuations and weak localization. A theoretical analysis of our experiments will enable to reach a deeper understanding of phase-coherent one-dimensional electronic motion in SWNTs.Comment: Replaced with published version. Minor changes in tex

Current-induced synchronized switching of magnetization

We investigate current-induced magnetization switching for a multilayer structure that allows a reduced switching current while maintaining high thermal stability of the magnetization. The structure consists of a perpendicular polarizer, a perpendicular free-layer, and an additional free-layer having in-plane magnetization. When the current runs perpendicular to the structure, the in-plane free-layer undergoes a precession and supplies an internal rf field to the perpendicular free-layer, resulting in a reduced switching current for one current polarity. For the other polarity, the in-plane free-layer almost saturates perpendicular to the plane and acts as another perpendicular polarizer, which also reduces the switching current.Comment: 18 pages, 4 figure

Galaxy pairs as a probe for mergers at z ~ 2

In this work I investigate the redshift evolution of pair fraction of a sample of 196 massive galaxies from z = 0 to 3, selected from the COSMOS field. We find that on average a massive galaxy undergoes ~ 1.1 \pm 0.5 major merger since z = 3. I will review the current limitations of using the pair fraction as a probe for quantifying the impact of mergers on galaxy evolution. This work is based on the paper Man et al. (2011).Comment: 4 pages; to appear on the Conference Proceedings for "Galaxy Mergers in an Evolving Universe", held in Hualien, Taiwan (October 2011

Quantum discord amplification induced by quantum phase transition via a cavity-Bose-Einstein-condensate system

We propose a theoretical scheme to realize a sensitive amplification of quantum discord (QD) between two atomic qubits via a cavity-Bose-Einstein condensate (BEC) system which was used to firstly realize the Dicke quantum phase transition (QPT) [Nature 464, 1301 (2010)]. It is shown that the influence of the cavity-BEC system upon the two qubits is equivalent to a phase decoherence environment. It is found that QPT in the cavity-BEC system is the physical mechanism of the sensitive QD amplification.Comment: 5 pages, 3 figure

On the Origin of Pluto's Small Satellites by Resonant Transport

The orbits of Pluto's four small satellites (Styx, Nix, Kerberos, and Hydra) are nearly circular and coplanar with the orbit of the large satellite Charon, with orbital periods nearly in the ratios 3:1, 4:1, 5:1, and 6:1 with Charon's orbital period. These properties suggest that the small satellites were created during the same impact event that placed Charon in orbit and had been pushed to their current positions by being locked in mean-motion resonances with Charon as Charon's orbit was expanded by tidal interactions with Pluto. Using the Pluto-Charon tidal evolution models developed by Cheng et al. (2014), we show that stable capture and transport of a test particle in multiple resonances at the same mean-motion commensurability is possible at the 5:1, 6:1, and 7:1 commensurabilities, if Pluto's zonal harmonic $J_{2P} = 0$. However, the test particle has significant orbital eccentricity at the end of the tidal evolution of Pluto-Charon in almost all cases, and there are no stable captures and transports at the 3:1 and 4:1 commensurabilities. Furthermore, a non-zero hydrostatic value of $J_{2P}$ destroys the conditions necessary for multiple resonance migration. Simulations with finite but minimal masses of Nix and Hydra also fail to yield any survivors. We conclude that the placing of the small satellites at their current orbital positions by resonant transport is extremely unlikely.Comment: 22 pages, including 7 figures; accepted for publication in Icaru