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

Collisional cooling of ultra-cold atom ensembles using Feshbach resonances

We propose a new type of cooling mechanism for ultra-cold fermionic atom ensembles, which capitalizes on the energy dependence of inelastic collisions in the presence of a Feshbach resonance. We first discuss the case of a single magnetic resonance, and find that the final temperature and the cooling rate is limited by the width of the resonance. A concrete example, based on a p-wave resonance of $^{40}$K, is given. We then improve upon this setup by using both a very sharp optical or radio-frequency induced resonance and a very broad magnetic resonance and show that one can improve upon temperatures reached with current technologies.Comment: 4 pages, 3 figure

Cancellation of light-shifts in an N-resonance clock

We demonstrate that first-order light-shifts can be cancelled for an all-optical, three-photon-absorption resonance ("N-resonance") on the D1 transition of Rb87. This light-shift cancellation enables improved frequency stability for an N-resonance clock. For example, using a table-top apparatus designed for N-resonance spectroscopy, we measured a short-term fractional frequency stability (Allan deviation) 1.5e-11 tau^(-1/2) for observation times 1s< tau < 50s. Further improvements in frequency stability should be possible with an apparatus designed as a dedicated N-resonance clock.Comment: 4 pages, 4 figure

Dynamical resonance locking in tidally interacting binary systems

We examine the dynamics of resonance locking in detached, tidally interacting binary systems. In a resonance lock, a given stellar or planetary mode is trapped in a highly resonant state for an extended period of time, during which the spin and orbital frequencies vary in concert to maintain the resonance. This phenomenon is qualitatively similar to resonance capture in planetary dynamics. We show that resonance locks can accelerate the course of tidal evolution in eccentric systems and also efficiently couple spin and orbital evolution in circular binaries. Previous analyses of resonance locking have not treated the mode amplitude as a fully dynamical variable, but rather assumed the adiabatic (i.e. Lorentzian) approximation valid only in the limit of relatively strong mode damping. We relax this approximation, analytically derive conditions under which the fixed point associated with resonance locking is stable, and further check these analytic results using numerical integrations of the coupled mode, spin, and orbital evolution equations. These show that resonance locking can sometimes take the form of complex limit cycles or even chaotic trajectories. We provide simple analytic formulae that define the binary and mode parameter regimes in which resonance locks of some kind occur (stable, limit cycle, or chaotic). We briefly discuss the astrophysical implications of our results for white dwarf and neutron star binaries as well as eccentric stellar binaries.Comment: 16 pages, 11 figure

Stochastic Resonance Can Drive Adaptive Physiological Processes

Stochastic resonance (SR) is a concept from the physics and engineering communities that has applicability to both systems physiology and other living systems. In this paper, it will be argued that stochastic resonance plays a role in driving behavior in neuromechanical systems. The theory of stochastic resonance will be discussed, followed by a series of expected outcomes, and two tests of stochastic resonance in an experimental setting. These tests are exploratory in nature, and provide a means to parameterize systems that couple biological and mechanical components. Finally, the potential role of stochastic resonance in adaptive physiological systems will be discussed

Lifetime of molecule-atom mixtures near a Feshbach resonance in 40K

We report a dramatic magnetic field dependence in the lifetime of trapped, ultracold diatomic molecules created through an s-wave Feshbach resonance in 40K. The molecule lifetime increases from less than 1 ms away from the Feshbach resonance to greater than 100 ms near resonance. We also have measured the trapped atom lifetime as a function of magnetic field near the Feshbach resonance; we find that the atom loss is more pronounced on the side of the resonance containing the molecular bound state

Partial Averaging Near a Resonance in Planetary Dynamics

Following the general numerical analysis of Melita and Woolfson (1996), I showed in a recent paper that a restricted, planar, circular planetary system consisting of Sun, Jupiter and Saturn would be captured in a near (2:1) resonance when one would allow for frictional dissipation due to interplanetary medium (Haghighipour, 1998). In order to analytically explain this resonance phenomenon, the method of partial averaging near a resonance was utilized and the dynamics of the first-order partially averaged system at resonance was studied. Although in this manner, the finding that resonance lock occurs for all initial relative positions of Jupiter and Saturn was confirmed, the first-order partially averaged system at resonance did not provide a complete picture of the evolutionary dynamics of the system and the similarity between the dynamical behavior of the averaged system and the main planetary system held only for short time intervals. To overcome these limitations, the method of partial averaging near a resonance is extended to the second order of perturbation in this paper and a complete picture of dynamical behavior of the system at resonance is presented. I show in this study that the dynamics of the second-order partially averaged system at resonance resembles the dynamical evolution of the main system during the resonance lock in general, and I present analytical explanations for the evolution of the orbital elements of the main system while captured in resonance.Comment: Plain TeX, 21 Pages, 6 Figures, Submitted to Celest.Mech.Dynamic.Astr

Alternative Route to Strong Interaction: Narrow Feshbach Resonance

We show that a narrow resonance produces strong interaction effects far beyond its width on the side of the resonance where the bound state has not been formed. This is due to a resonance structure of its phase shift, which shifts the phase of a large number of scattering states by $\pi$ before the bound state emerges. As a result, the magnitude of the interaction energy when approaching the resonance on the "upper" and "lower" branch from different side of the resonance is highly asymmetric, unlike their counter part in wide resonances. Measurements of these effects are experimentally feasible.Comment: 4 pages, 5 figure