Mean-field dynamics of a Bose-Einstein condensate in a time-dependent triple-well trap: Nonlinear eigenstates, Landau-Zener models and STIRAP

We investigate the dynamics of a Bose--Einstein condensate (BEC) in a triple-well trap in a three-level approximation. The inter-atomic interactions are taken into account in a mean-field approximation (Gross-Pitaevskii equation), leading to a nonlinear three-level model. New eigenstates emerge due to the nonlinearity, depending on the system parameters. Adiabaticity breaks down if such a nonlinear eigenstate disappears when the parameters are varied. The dynamical implications of this loss of adiabaticity are analyzed for two important special cases: A three level Landau-Zener model and the STIRAP scheme. We discuss the emergence of looped levels for an equal-slope Landau-Zener model. The Zener tunneling probability does not tend to zero in the adiabatic limit and shows pronounced oscillations as a function of the velocity of the parameter variation. Furthermore we generalize the STIRAP scheme for adiabatic coherent population transfer between atomic states to the nonlinear case. It is shown that STIRAP breaks down if the nonlinearity exceeds the detuning.Comment: RevTex4, 7 pages, 11 figures, content extended and title/abstract change

Proceedings of the 35th Annual Meeting, Southern Soybean Disease Workers (March 12-13, 2008, Pensacola, Florida)

Contents Southern United States Soybean Disease Loss Estimate for 2007. Compiled by SR Koenning Contributed papers (Clayton Hollier, moderator) Effects of Row Spacing and Leaf Wetness on the Temporal and Spatial Spread of Soybean Rust within Soybean Canopies. DF Narváez, JJ Marois, DL Wright, and S Isard Effects of Potassium, Chloride, and Minor Elements Nutrition on Asian Soybean Rust. RW Schneider, EP Mumma, CL Clark, and CG Giles The Impact of Selected Fungicide Treatments on Disease Progress of Asian Soybean Rust and Other Diseases of Soybean. GB Padgett, MA Purvis, A Hogan, and S Martin Soybean Sudden Death Syndrome Variety Testing at Southern Illinois University. C Herzog, C Schmidt, and M Schmidt Soybean Yield Suppression Due to Diseases for the Top Eight Soybean-Producing Countries in 2006. A Wrather, S Koenning, R Balardin, LH Carregal, R Escobar, GK Gupta, Z Ma, W Morel, LD Ploper, and A Tenuta Impact of Frogeye Leaf Spot on Soybean Yield in the Lower Midwest. CM Vick, AK Vick, JP Bond, and JA Wrather Graduate student papers (Alemu Mengistu, moderator) Laboratory Evaluation of Soybean Resistance to Pod Blight Caused by Cercospora kikuchii. BC Wells and GL Sciumbato Temporal Dynamics of Root and Foliar Symptoms of Soybean Sudden Death Syndrome at Different Inoculum Densities. C Gongora-Canul, FW Nutter, Jr, and LFS Leandro Discussion session (Allen Wrather, moderator) Soybean Rust Sentinal Survey discussion. Don Hershman Proceedings of the Southern Soybean Disease Workers are published annually by the Southern Soybean Disease Workers. Text, references, figures, and tables are reproduced as they were submitted by authors. The opinions expressed by the participants at this conference are their own and do not necessarily represent those of the Southern Soybean Disease Workers. Mention of a trademark or proprietary products in this publication does not constitute a guarantee, warranty, or endorsement of that product by the Southern Soybean Disease Workers

Effects of a localized beam on the dynamics of excitable cavity solitons

We study the dynamical behavior of dissipative solitons in an optical cavity filled with a Kerr medium when a localized beam is applied on top of the homogeneous pumping. In particular, we report on the excitability regime that cavity solitons exhibits which is emergent property since the system is not locally excitable. The resulting scenario differs in an important way from the case of a purely homogeneous pump and now two different excitable regimes, both Class I, are shown. The whole scenario is presented and discussed, showing that it is organized by three codimension-2 points. Moreover, the localized beam can be used to control important features, such as the excitable threshold, improving the possibilities for the experimental observation of this phenomenon.Comment: 9 Pages, 12 figure

Topological classification of black Hole: Generic Maxwell set and crease set of horizon

The crease set of an event horizon or a Cauchy horizon is an important object which determines qualitative properties of the horizon. In particular, it determines the possible topologies of the spatial sections of the horizon. By Fermat's principle in geometric optics, we relate the crease set and the Maxwell set of a smooth function in the context of singularity theory. We thereby give a classification of generic topological structure of the Maxwell sets and the generic topologies of the spatial section of the horizon.Comment: 22 pages, 6 figure

Dynamics and Thermodynamics of Systems with Long Range Interactions: an Introduction

We review theoretical results obtained recently in the framework of statistical mechanics to study systems with long range forces. This fundamental and methodological study leads us to consider the different domains of applications in a trans-disciplinary perspective (astrophysics, nuclear physics, plasmas physics, metallic clusters, hydrodynamics,...) with a special emphasis on Bose-Einstein condensates.Comment: Chapter of the forthcoming "Lecture Notes in Physics" volume: ``Dynamics and Thermodynamics of Systems with Long Range Interactions'', T. Dauxois, S. Ruffo, E. Arimondo, M. Wilkens Eds., Lecture Notes in Physics Vol. 602, Springer (2002). (see http://link.springer.de/series/lnpp/

Resonances in a spring-pendulum: algorithms for equivariant singularity theory

A spring-pendulum in resonance is a time-independent Hamiltonian model system for formal reduction to one degree of freedom, where some symmetry (reversibility) is maintained. The reduction is handled by equivariant singularity theory with a distinguished parameter, yielding an integrable approximation of the Poincaré map. This makes a concise description of certain bifurcations possible. The computation of reparametrizations from normal form to the actual system is performed by Gröbner basis techniques.

Mechanism of Deep-focus Earthquakes Anomalous Statistics

Analyzing the NEIC-data we have shown that the spatial deep-focus earthquake distribution in the Earth interior over the 1993-2006 is characterized by the clearly defined periodical fine discrete structure with period L=50 km, which is solely generated by earthquakes with magnitude M 3.9 to 5.3 and only on the convergent boundary of plates. To describe the formation of this structure we used the model of complex systems by A. Volynskii and S. Bazhenov. The key property of this model consists in the presence of a rigid coating on a soft substratum. It is shown that in subduction processes the role of a rigid coating plays the slab substance (lithosphere) and the upper mantle acts as a soft substratum. Within the framework of this model we have obtained the estimation of average values of stress in the upper mantle and Young's modulus for the oceanic slab (lithosphere) and upper mantle.Comment: 9 pages, 7 figure

Soft X-ray harmonic comb from relativistic electron spikes

We demonstrate a new high-order harmonic generation mechanism reaching the `water window' spectral region in experiments with multi-terawatt femtosecond lasers irradiating gas jets. A few hundred harmonic orders are resolved, giving uJ/sr pulses. Harmonics are collectively emitted by an oscillating electron spike formed at the joint of the boundaries of a cavity and bow wave created by a relativistically self-focusing laser in underdense plasma. The spike sharpness and stability are explained by catastrophe theory. The mechanism is corroborated by particle-in-cell simulations

Fuzzy Geometry of Phase Space and Quantization of Massive Fields

The quantum space-time and the phase space with fuzzy structure is investigated as the possible quantization formalism. In this theory the state of nonrelativistic particle corresponds to the element of fuzzy ordered set (Foset) - fuzzy point. Due to Foset partial (weak) ordering, particle's space coordinate x acquires principal uncertainty dx. It's shown that Shroedinger formalism of Quantum Mechanics can be completely derived from consideration of particle evolution in fuzzy phase space with minimal number of axioms.Comment: 13 pages, Talk given at QFEXT07 Workshop, Leipzig, Sept. 200

Semiclassical ionization dynamics of the hydrogen molecular ion in an electric field of arbitrary orientation

Quasi-static models of barrier suppression have played a major role in our understanding of the ionization of atoms and molecules in strong laser fields. Despite their success, in the case of diatomic molecules these studies have so far been restricted to fields aligned with the molecular axis. In this paper we investigate the locations and heights of the potential barriers in the hydrogen molecular ion in an electric field of arbitrary orientation. We find that the barriers undergo bifurcations as the external field strength and direction are varied. This phenomenon represents an unexpected level of intricacy even on this most elementary level of the dynamics. We describe the dynamics of tunnelling ionization through the barriers semiclassically and use our results to shed new light on the success of a recent theory of molecular tunnelling ionization as well as earlier theories that restrict the electric field to be aligned with the molecular axis