Canonical Transformation Approach to the Ultrafast Non-linear Optical Dynamics of Semiconductors

We develop a theory describing the effects of many-particle Coulomb correlations on the coherent ultrafast nonlinear optical response of semiconductors and metals. Our approach is based on a mapping of the nonlinear optical response of the ``bare'' system onto the linear response of a ``dressed'' system. The latter is characterized by effective time-dependent optical transition matrix elements, electron/hole dispersions, and interaction potentials, which in undoped semiconductors are determined by the single-exciton and two-exciton Green functions in the absence of optical fields. This mapping is achieved by eliminating the optically-induced charge fluctuations from the Hamiltonian using a Van Vleck canonical transformation. It takes into account all many-body contributions up to a given order in the optical fields as well as important Coulomb-induced quantum dynamics to all orders in the optical field. Our approach allows us to distinguish between optical nonlinearities of different origins and provides a physically-intuitive interpretation of their manifestations in ultrafast coherent nonlinear optical spectroscopy.Comment: 24 page

Effects of Direct Instruction and Environmentally Designed Instruction on the Process and Product Characteristics of a Fundamental Skill

This study investigated the effects of direct instruction and an environmentally designed instructional strategy on the product and process characteristics of kindergarten and second grade children in the standing long jump. One hundred and sixteen kindergarten and second grade students participated in the study and were assigned to a 3-day, 60-trial, direct instruction group or a 3-day, 60-trial, environmentally designed instruction group. A pretest, posttest, and retention test were administered in a flat mat testing condition and one designed to elicit performance through the testing environment (the swamp). Both instructional intervention groups were different from the control group at the posttest and the retention test. Younger students, less skilled students, and students tested at the pretest benefited most from the environmental testing condition. With age, skill, and experience the environmental testing condition lost its advantage. The instructional interventions had different effects on the process characteristics of the jump

Vortices on Hyperbolic Surfaces

It is shown that abelian Higgs vortices on a hyperbolic surface $M$ can be constructed geometrically from holomorphic maps $f:M \to N$, where $N$ is also a hyperbolic surface. The fields depend on $f$ and on the metrics of $M$ and $N$. The vortex centres are the ramification points, where the derivative of $f$ vanishes. The magnitude of the Higgs field measures the extent to which $f$ is locally an isometry. Witten's construction of vortices on the hyperbolic plane is rederived, and new examples of vortices on compact surfaces and on hyperbolic surfaces of revolution are obtained. The interpretation of these solutions as SO(3)-invariant, self-dual SU(2) Yang--Mills fields on $\R^4$ is also given.Comment: Revised version: new section on four-dimensional interpretation of hyperbolic vortices added

Tactical and Skill Approaches to Teaching Sport and Games

Physical education teachers have long been concerned with issues relating to how to best teach sports and games to students. The ultimate goal of sport instruction is to enable students to enjoy participation and to play the game reasonably well so that they will have increased motivation to play and gain the benefits of participation. This monograph describes the efforts of a group of researchers to investigate issues relative to teaching and learning sport in a physical education setting. More specifically, the authors of this monograph investigate what students are likely to learn and not learn as a result of a skill approach, a tactical awareness approach, and a combined tactical and skill approach to teaching badminton