Asymptotic stability at infinity for differentiable vector fields of the plane

Let X:R2\Dr->R2 be a differentiable (but not necessarily C1) vector field, where r>0 and Dr={z\in R2:|z|\le r}. If for some e>0 and for all p\in R2\Dr, no eigenvalue of D_p X belongs to (-e,0]\cup {z\in\C:\mathcal{R}(z)\ge 0}, then (a)For all p\in R2\Dr, there is a unique positive semi--trajectory of X starting at p; (b)\mathcal{I}(X), the index of X at infinity, is a well defined number of the extended real line [-\infty,\infty); (c) There exists a constant vector v\in R2 such that if \mathcal{I}(X) is less than zero (resp. greater or equal to zero), then the point at infinity \infty of the Riemann sphere R2\cup\set{\infty} is a repellor (resp. an attractor) of the vector field X+v.Comment: 16 pages, 7 figure

Observation of the Quantum Zeno and Anti-Zeno effects in an unstable system

We report the first observation of the Quantum Zeno and Anti-Zeno effects in an unstable system. Cold sodium atoms are trapped in a far-detuned standing wave of light that is accelerated for a controlled duration. For a large acceleration the atoms can escape the trapping potential via tunneling. Initially the number of trapped atoms shows strong non-exponential decay features, evolving into the characteristic exponential decay behavior. We repeatedly measure the number of atoms remaining trapped during the initial period of non-exponential decay. Depending on the frequency of measurements we observe a decay that is suppressed or enhanced as compared to the unperturbed system.Comment: 4 pages, 5 figures, submitted to PR

Affine interval exchange transformations with flips and wandering intervals

There exist uniquely ergodic affine interval exchange transformations of [0,1] with flips having wandering intervals and such that the support of the invariant measure is a Cantor set.Comment: 7 page

Experimental Study of the Role of Atomic Interactions on Quantum Transport

We report an experimental study of quantum transport for atoms confined in a periodic potential and compare between thermal and BEC initial conditions. We observe ballistic transport for all values of well depth and initial conditions, and the measured expansion velocity for thermal atoms is in excellent agreement with a single-particle model. For weak wells, the expansion of the BEC is also in excellent agreement with single-particle theory, using an effective temperature. We observe a crossover to a new regime for the BEC case as the well depth is increased, indicating the importance of interactions on quantum transport.Comment: 4 pages, 3 figure

Unique ergodicity of circle and interval exchange transformations with flips

We study the existence of transitive exchange maps with flips defined on the unit circle. We provide a complete answer to the question of whether there exists a transitive exchange map of the unit circle defined on n subintervals and having f flips.Comment: 13 pages, 6 figures; notational changes, smaller figure

Local mapping of dissipative vortex motion

We explore, with unprecedented single vortex resolution, the dissipation and motion of vortices in a superconducting ribbon under the influence of an external alternating magnetic field. This is achieved by combing the phase sensitive character of ac-susceptibility, allowing to distinguish between the inductive-and dissipative response, with the local power of scanning Hall probe microscopy. Whereas the induced reversible screening currents contribute only inductively, the vortices do leave a fingerprint in the out-of-phase component. The observed large phase-lag demonstrates the dissipation of vortices at timescales comparable to the period of the driving force (i.e. 13 ms). These results indicate the presence of slow microscopic loss mechanisms mediated by thermally activated hopping transport of vortices between metastable states.Comment: 5 pages, 2 figure

Behavioral Risks for West Nile Virus Disease, Northern Colorado, 2003

Protective practices may affect the level of illness in a community