The Resonance Overlap and Hill Stability Criteria Revisited

We review the orbital stability of the planar circular restricted three-body problem, in the case of massless particles initially located between both massive bodies. We present new estimates of the resonance overlap criterion and the Hill stability limit, and compare their predictions with detailed dynamical maps constructed with N-body simulations. We show that the boundary between (Hill) stable and unstable orbits is not smooth but characterized by a rich structure generated by the superposition of different mean-motion resonances which does not allow for a simple global expression for stability. We propose that, for a given perturbing mass $m_1$ and initial eccentricity $e$, there are actually two critical values of the semimajor axis. All values $a a_{\rm unstable}$ are unstable in the Hill sense. The first limit is given by the Hill-stability criterion and is a function of the eccentricity. The second limit is virtually insensitive to the initial eccentricity, and closely resembles a new resonance overlap condition (for circular orbits) developed in terms of the intersection between first and second-order mean-motion resonances.Comment: 33 pages, 14 figures, accepte

Kinetic Theory of Collisionless Self-Gravitating Gases: II. Relativistic Corrections in Galactic Dynamics

In this paper we study the kinetic theory of many-particle astrophysical systems imposing axial symmetry and extending our previous analysis in Phys. Rev. D 83, 123007 (2011). Starting from a Newtonian model describing a collisionless self-gravitating gas, we develop a framework to include systematically the first general relativistic corrections to the matter distribution and gravitational potentials for general stationary systems. Then, we use our method to obtain particular solutions for the case of the Morgan & Morgan disks. The models obtained are fully analytical and correspond to the post-Newtonian generalizations of classical ones. We explore some properties of the models in order to estimate the importance of post-Newtonian corrections and we find that, contrary to the expectations, the main modifications appear far from the galaxy cores. As a by-product of this investigation we derive the corrected version of the tensor virial theorem. For stationary systems we recover the same result as in the Newtonian theory. However, for time dependent backgrounds we find that there is an extra piece that contributes to the variation of the inertia tensor.Comment: 30 pages, 8 figures. v2: Minor corrections and references added. Conclusions unchanged. v3: Version published in PR

Conductance peaks in open quantum dots

We present a simple measure of the conductance fluctuations in open ballistic chaotic quantum dots, extending the number of maxima method originally proposed for the statistical analysis of compound nuclear reactions. The average number of extreme points (maxima and minima) in the dimensionless conductance, $T$, as a function of an arbitrary external parameter $Z$, is directly related to the autocorrelation function of $T(Z)$. The parameter $Z$ can be associated to an applied gate voltage causing shape deformation in quantum dot, an external magnetic field, the Fermi energy, etc.. The average density of maxima is found to be $= \alpha_{Z}/Z_c$, where $\alpha_{Z}$ is a universal constant and $Z_c$ is the conductance autocorrelation length, which is system specific. The analysis of $$ does not require large statistic samples, providing a quite amenable way to access information about parametric correlations, such as $Z_c$.Comment: 5 pages, 5 figures, accepted to be published - Physical Review Letter

Dynamical transitions and sliding friction of the phase-field-crystal model with pinning

We study the nonlinear driven response and sliding friction behavior of the phase-field-crystal (PFC) model with pinning including both thermal fluctuations and inertial effects. The model provides a continuous description of adsorbed layers on a substrate under the action of an external driving force at finite temperatures, allowing for both elastic and plastic deformations. We derive general stochastic dynamical equations for the particle and momentum densities including both thermal fluctuations and inertial effects. The resulting coupled equations for the PFC model are studied numerically. At sufficiently low temperatures we find that the velocity response of an initially pinned commensurate layer shows hysteresis with dynamical melting and freezing transitions for increasing and decreasing applied forces at different critical values. The main features of the nonlinear response in the PFC model are similar to the results obtained previously with molecular dynamics simulations of particle models for adsorbed layers.Comment: 7 pages, 8 figures, to appear in Physcial Review

Kinetic Theory of Collisionless Self-Gravitating Gases: Post-Newtonian Polytropes

In this paper we study the kinetic theory of many-particle astrophysical systems and we present a consistent version of the collisionless Boltzmann equation in the 1PN approximation. We argue that the equation presented by Rezania and Sobouti in A&A 354 1110 (2000) is not the correct expression to describe the evolution of a collisionless self-gravitating gas. One of the reasons that account for the previous statement is that the energy of a free-falling test particle, obeying the 1PN equations of motion for static gravitational fields, is not a static solution of the mentioned equation. The same statement holds for the angular momentum, in the case of spherical systems. We provide the necessary corrections and obtain an equation that is consistent with the corresponding equations of motion and the 1PN conserved quantities. We suggest some potential relevance for the study of high density astrophysical systems and as an application we construct the corrected version of the post-Newtonian polytropes.Comment: 23 pages, 24 figures. Accepted for publication in PR

Comparison of coherence times in three dc SQUID phase qubits

We report measurements of spectroscopic linewidth and Rabi oscillations in three thin-film dc SQUID phase qubits. One device had a single-turn Al loop, the second had a 6-turn Nb loop, and the third was a first order gradiometer formed from 6-turn wound and counter-wound Nb coils to provide isolation from spatially uniform flux noise. In the 6 - 7.2 GHz range, the spectroscopic coherence times for the gradiometer varied from 4 ns to 8 ns, about the same as for the other devices (4 to 10 ns). The time constant for decay of Rabi oscillations was significantly longer in the single-turn Al device (20 to 30 ns) than either of the Nb devices (10 to 15 ns). These results imply that spatially uniform flux noise is not the main source of decoherence or inhomogenous broadening in these devices.Comment: 4 pages, 5 figures, accepted for publication in IEEE Trans. Appl. Supercon