Rational Map of CP^2 with No Invariant Foliation

Conference Poster presented at: Midwest Dynamical Systems Conference, Champaign/Urbana, IL November 1-3, 2013

Rational Maps of CP^2 with No Invariant Foliation

We present simple examples of rational maps of the complex projective plane with equal first and second dynamical degrees and no invariant foliation

Photon-number-resolution with sub-30-ps timing using multi-element superconducting nanowire single photon detectors

A photon-number-resolving detector based on a four-element superconducting nanowire single photon detector is demonstrated to have sub-30-ps resolution in measuring the arrival time of individual photons. This detector can be used to characterize the photon statistics of non-pulsed light sources and to mitigate dead-time effects in high-speed photon counting applications. Furthermore, a 25% system detection efficiency at 1550 nm was demonstrated, making the detector useful for both low-flux source characterization and high-speed photon-counting and quantum communication applications. The design, fabrication and testing of this detector are described, and a comparison between the measured and theoretical performance is presented.Comment: 13 pages, 5 figure

Exact soliton solutions of coupled nonlinear Schr\"odinger equations: Shape changing collisions, logic gates and partially coherent solitons

The novel dynamical features underlying soliton interactions in coupled nonlinear Schr{\"o}dinger equations, which model multimode wave propagation under varied physical situations in nonlinear optics, are studied. In this paper, by explicitly constructing multisoliton solutions (upto four-soliton solutions) for two coupled and arbitrary $N$-coupled nonlinear Schr{\"o}dinger equations using the Hirota bilinearization method, we bring out clearly the various features underlying the fascinating shape changing (intensity redistribution) collisions of solitons, including changes in amplitudes, phases and relative separation distances, and the very many possibilities of energy redistributions among the modes of solitons. However in this multisoliton collision process the pair-wise collision nature is shown to be preserved in spite of the changes in the amplitudes and phases of the solitons. Detailed asymptotic analysis also shows that when solitons undergo multiple collisions, there exists the exciting possibility of shape restoration of atleast one soliton during interactions of more than two solitons represented by three and higher order soliton solutions. From application point of view, we have shown from the asymptotic expressions how the amplitude (intensity) redistribution can be written as a generalized linear fractional transformation for the $N$-component case. Also we indicate how the multisolitons can be reinterpreted as various logic gates for suitable choices of the soliton parameters, leading to possible multistate logic. In addition, we point out that the various recently studied partially coherent solitons are just special cases of the bright soliton solutions exhibiting shape changing collisions, thereby explaining their variable profile and shape variation in collision process.Comment: 50 Pages, 13 .jpg figures. To appear in PR

Resonance Effects in the Nonadiabatic Nonlinear Quantum Dimer

The quantum nonlinear dimer consisting of an electron shuttling between the two sites and in weak interaction with vibrations, is studied numerically under the application of a DC electric field. A field-induced resonance phenomenon between the vibrations and the electronic oscillations is found to influence the electronic transport greatly. For initially delocalization of the electron, the resonance has the effect of a dramatic increase in the transport. Nonlinear frequency mixing is identified as the main mechanism that influences transport. A characterization of the frequency spectrum is also presented.Comment: 7 pages, 6 figure

Simple method for excitation of a Bose-Einstein condensate

An appropriate, time-dependent modification of the trapping potential may be sufficient to create effectively collective excitations in a cold atom Bose-Einstein condensate. The proposed method is complementary to earlier suggestions and should allow the creation of both dark solitons and vortices.Comment: 8 pages, 7 figures, version accepted for publication in Phys. Rev.

Europe as a multilevel federation

Peer reviewedPublisher PD

Application of PILATUS II Detector Modules for High Resolution X-Ray Imaging Crystal Spectrometers on the Alcator C-Mod Tokamak

A new type of X-ray imaging crystal spectrometer for Doppler measurements of the radial profiles of the ion temperature and plasma rotation velocity in tokamak plasmas is presently being developed in a collaboration between various laboratories. The spectrometer will consist of a spherically bent crystal and a two-dimensional position sensitive detector; and it will record temporally and spatially resolved X-ray line spectra from highly-charged ions. The detector must satisfy challenging requirements with respect to count rate and spatial resolution. The paper presents the results from a recent test of a PILATUS II detector module on Alcator C-Mod, which demonstrate that the PILATUS II detector modules will satisfy these requirements

Supersymmetric Relations Among Electromagnetic Dipole Operators

Supersymmetric contributions to all leptonic electromagnetic dipole operators have essentially identical diagramatic structure. With approximate slepton universality this allows the muon anomalous magnetic moment to be related to the electron electric dipole moment in terms of supersymmetric phases, and to radiative flavor changing lepton decays in terms of small violations of slepton universality. If the current discrepancy between the measured and Standard Model values of the muon anomalous magnetic moment is due to supersymmetry, the current bound on the electron electric dipole moment then implies that the phase of the electric dipole operator is less than $2 \times 10^{-3}$. Likewise the current bound on $\mu \to e \gamma$ decay implies that the fractional selectron-smuon mixing in the left-left mass squared matrix, \delta m_{\smuon \selectron}^2 / m_{\slepton}^2, is less than $10^{-4}$. These relations and constraints are fairly insensitive to details of the superpartner spectrum for moderate to large $\tan \beta$.Comment: Latex, 38 pages, 2 figure

PREDICTING THE SUMMER TEMPERATURE OF SMALL STREAMS IN SOUTHWESTERN WISCONSIN 1

One of the biggest challenges in managing cold water streams in the Midwest is understanding how stream temperature is controlled by the complex interactions among meteorologic processes, channel geometry, and ground water inflow. Inflow of cold ground water, shade provided by riparian vegetation, and channel width are the most important factors controlling summer stream temperatures. A simple screening model was used to quantitatively evaluate the importance of these factors and guide management decisions. The model uses an analytical solution to the heat transport equation to predict steady-state temperature throughout a stream reach. The model matches field data from four streams in southwestern Wisconsin quite well (typically within 1°C) and helps explain the observed warming and cooling trends along each stream reach. The distribution of ground water inflow throughout a stream reach has an important influence on stream temperature, and springs are especially effective at providing thermal refuge for fish. Although simple, this model provides insight into the importance of ground water and the impact different management strategies, such as planting trees to increase shade, may have on summer stream temperature.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/74032/1/j.1752-1688.2005.tb03714.x.pd