Retrograde resonance in the planar three-body problem

We continue the investigation of the dynamics of retrograde resonances initiated in Morais & Giuppone (2012). After deriving a procedure to deduce the retrograde resonance terms from the standard expansion of the three-dimensional disturbing function, we concentrate on the planar problem and construct surfaces of section that explore phase-space in the vicinity of the main retrograde resonances (2/-1, 1/-1 and 1/-2). In the case of the 1/-1 resonance for which the standard expansion is not adequate to describe the dynamics, we develop a semi-analytic model based on numerical averaging of the unexpanded disturbing function, and show that the predicted libration modes are in agreement with the behavior seen in the surfaces of section.Comment: Celestial Mechanics and Dynamical Astronomy, in pres

Asteroids in retrograde resonance with Jupiter and Saturn

We identify a set of asteroids among Centaurs and Damocloids, that orbit contrary to the common direction of motion in the Solar System and that enter into resonance with Jupiter and Saturn. Their orbits have inclinations I >= 140 deg and semi-major axes a < 15 AU. Two objects are currently in retrograde resonance with Jupiter: 2006 BZ8 in the 2/-5 resonance and 2008 SO218 in the 1/-2 resonance. One object, 2009 QY6, is currently in the 2/-3 retrograde resonance with Saturn. These are the first examples of Solar System objects in retrograde resonance. The present resonant configurations last for several thousand years. Brief captures in retrograde resonance with Saturn are also possible during the 20,000 years integration timespan, particularly in the 1/-1 resonance (2006 BZ8) and the 9/-7 resonance (1999 LE31).Comment: 6 pages, 7 figures, accepted for publication in MNRAS Letter

Stellar wobble caused by a nearby binary system: eccentric and inclined orbits

Most extrasolar planets currently known were discovered by means of an indirect method that measures the stellar wobble caused by the planet. We previously studied a triple system composed of a star and a nearby binary on circular coplanar orbits. We showed that although the effect of the binary on the star can be differentiated from the stellar wobble caused by a planet, because of observational limitations the two effects may often remain indistinguishable. Here, we develop a model that applies to eccentric and inclined orbits. We show that the binary's effect is more likely to be mistaken by planet(s) in the case of coplanar motion observed equator-on. Moreover, when the orbits are eccentric, the magnitude of the binary's effect may be larger than in the circular case. Additionally, an eccentric binary can mimic two planets with orbital periods in the ratio 2/1. However, when the star's orbit around the binary's center of mass has a high eccentricity and a reasonably well-constrained period, it should be easier to distinguish the binary's effect from a planet.Comment: 10 pages, 9 figures, 2 table

Correlated versus Uncorrelated Stripe Pinning: the Roles of Nd and Zn Co-Doping

We investigate the stripe pinning produced by Nd and Zn co-dopants in cuprates via a renormalization group approach. The two dopants play fundamentally different roles in the pinning process. While Nd induces a correlated pinning potential that traps the stripes in a flat phase and suppresses fluctuations, Zn pins the stripes in a disordered manner and promotes line meandering. We obtain the zero temperature phase diagram and compare our results with neutron scattering data. A good agreement is found between theory and experiment.Comment: To appear at the proceedings of the LLD2K Conference Tsukuba, July 2000, Japan. 4 pages, 2 figure

Genesis of the Floquet Hofstadter butterfly

We investigate theoretically the spectrum of a graphene-like sample (honeycomb lattice) subjected to a perpendicular magnetic field and irradiated by circularly polarized light. This system is studied using the Floquet formalism, and the resulting Hofstadter spectrum is analyzed for different regimes of the driving frequency. For lower frequencies, resonances of various copies of the spectrum lead to intricate formations of topological gaps. In the Landau-level regime, new wing-like gaps emerge upon reducing the driving frequency, thus revealing the possibility of dynamically tuning the formation of the Hofstadter butterfly. In this regime, an effective model may be analytically derived, which allows us to retrace the energy levels that exhibit avoided crossings and ultimately lead to gap structures with a wing-like shape. At high frequencies, we find that gaps open for various fluxes at $E=0$, and upon increasing the amplitude of the driving, gaps also close and reopen at other energies. The topological invariants of these gaps are calculated and the resulting spectrum is elucidated. We suggest opportunities for experimental realization and discuss similarities with Landau-level structures in non-driven systems.Comment: 8 pages, 4 figure

Proposed Spontaneous Generation of Magnetic Fields by Curved Layers of a Chiral Superconductor

We demonstrate that two-dimensional chiral superconductors on curved surfaces spontaneously develop magnetic flux. This geometric Meissner effect provides an unequivocal signature of chiral super- conductivity, which could be observed in layered materials under stress. We also employ the effect to explain some puzzling questions related to the location of zero-energy Majorana modes

A semi-empirical stability criterion for real planetary systems

We test a crossing orbit stability criterion for eccentric planetary systems, based on Wisdom's criterion of first order mean motion resonance overlap (Wisdom, 1980). We show that this criterion fits the stability regions in real exoplanet systems quite well. In addition, we show that elliptical orbits can remain stable even for regions where the apocenter distance of the inner orbit is larger than the pericenter distance of the outer orbit, as long as the initial orbits are aligned. The analytical expressions provided here can be used to put rapid constraints on the stability zones of multi-planetary systems. As a byproduct of this research, we further show that the amplitude variations of the eccentricity can be used as a fast-computing stability indicator.Comment: 11 pages, 11 figures. MNRAS accepte