On Cr−C^r-closing for flows on 2-manifolds

For some full measure subset B of the set of iet's (i.e. interval exchange transformations) the following is satisfied: Let X be a $C^r$, $1\le r\le \infty$, vector field, with finitely many singularities, on a compact orientable surface M. Given a nontrivial recurrent point $p\in M$ of X, the holonomy map around p is semi-conjugate to an iet $E :[0,1) \to [0,1).$ If $E\in B$ then there exists a $C^r$ vector field Y, arbitrarily close to X, in the $C^r-$topology, such that Y has a closed trajectory passing through p.Comment: 7 pages, 1 figur

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

A statistical approach to identify superluminous supernovae and probe their diversity

We investigate the identification of hydrogen-poor superluminous supernovae (SLSNe I) using a photometric analysis, without including an arbitrary magnitude threshold. We assemble a homogeneous sample of previously classified SLSNe I from the literature, and fit their light curves using Gaussian processes. From the fits, we identify four photometric parameters that have a high statistical significance when correlated, and combine them in a parameter space that conveys information on their luminosity and color evolution. This parameter space presents a new definition for SLSNe I, which can be used to analyse existing and future transient datasets. We find that 90% of previously classified SLSNe I meet our new definition. We also examine the evidence for two subclasses of SLSNe I, combining their photometric evolution with spectroscopic information, namely the photospheric velocity and its gradient. A cluster analysis reveals the presence of two distinct groups. `Fast' SLSNe show fast light curves and color evolution, large velocities, and a large velocity gradient. `Slow' SLSNe show slow light curve and color evolution, small expansion velocities, and an almost non-existent velocity gradient. Finally, we discuss the impact of our analyses in the understanding of the powering engine of SLSNe, and their implementation as cosmological probes in current and future surveys.Comment: 16 pages, 9 figures, accepted by ApJ on 23/01/201

Correcting symmetry imperfections in linear multipole traps

Multipole radio-frequency traps are central to collisional experiments in cryogenic environments. They also offer possibilities to generate new type of ion crystals topologies and in particular the potential to create infinite 1D/2D structures: ion rings and ion tubes. However, multipole traps have also been shown to be very sensitive to geometrical misalignment of the trap rods, leading to additional local trapping minima. The present work proposes a method to correct non-ideal potentials, by modifying the applied radio-frequency amplitudes for each trap rod. This approach is discussed for the octupole trap, leading to the restitution of the ideal Mexican-Hat-like pseudo-potential, expected in multipole traps. The goodness of the compensation method is quantified in terms of the choice of the diagnosis area, the residual trapping potential variations, the required adaptation of the applied radio-frequency voltage amplitudes, and the impact on the trapped ion structures. Experimental implementation for macroscopic multipole traps is also discussed, in order to propose a diagnostic method with respect to the resolution and stability of the trap drive. Using the proposed compensation technique, we discuss the feasibility of generating a homogeneous ion ring crystal, which is a measure of quality for the obtained potential well

Fast accumulation of ions in a dual trap

Transporting charged particles between different traps has become an important feature in high-precision spectroscopy experiments of different types. In many experiments in atomic and molecular physics, the optical probing of the ions is not carried out at the same location as the creation or state preparation. In our double linear radio-frequency trap, we have implemented a fast protocol allowing to shuttle large ion clouds very efficiently between traps, in times shorter than a millisecond. Moreover, our shuttling protocol is a one-way process, allowing to add ions to an existing cloud without loss of the already trapped sample. This feature makes accumulation possible, resulting in the creation of large ion clouds. Experimental results show, that ion clouds of large size are reached with laser-cooling, however, the described mechanism does not rely on any cooling process

A CrC^{r} Closing Lemma for a Class of Symplectic Diffeomorphisms

We prove a $C^r$ closing lemma for a class of partially hyperbolic symplectic diffeomorphisms. We show that for a generic $C^r$ symplectic diffeomorphism, $r =1, 2, ...,$, with two dimensional center and close to a product map, the set of all periodic points is dense

Nongauge bright soliton of the nonlinear Schrodinger (NLS) equation and a family of generalized NLS equations

We present an approach to the bright soliton solution of the NLS equation from the standpoint of introducing a constant potential term in the equation. We discuss a `nongauge' bright soliton for which both the envelope and the phase depend only on the traveling variable. We also construct a family of generalized NLS equations with solitonic sech^p solutions in the traveling variable and find an exact equivalence with other nonlinear equations, such as the Korteveg-de Vries and Benjamin-Bona-Mahony equations when p=2Comment: ~4 pages, 3 figures, 16 references, published versio