The one dimensional Kondo lattice model at partial band filling

The Kondo lattice model introduced in 1977 describes a lattice of localized magnetic moments interacting with a sea of conduction electrons. It is one of the most important canonical models in the study of a class of rare earth compounds, called heavy fermion systems, and as such has been studied intensively by a wide variety of techniques for more than a quarter of a century. This review focuses on the one dimensional case at partial band filling, in which the number of conduction electrons is less than the number of localized moments. The theoretical understanding, based on the bosonized solution, of the conventional Kondo lattice model is presented in great detail. This review divides naturally into two parts, the first relating to the description of the formalism, and the second to its application. After an all-inclusive description of the bosonization technique, the bosonized form of the Kondo lattice hamiltonian is constructed in detail. Next the double-exchange ordering, Kondo singlet formation, the RKKY interaction and spin polaron formation are described comprehensively. An in-depth analysis of the phase diagram follows, with special emphasis on the destruction of the ferromagnetic phase by spin-flip disorder scattering, and of recent numerical results. The results are shown to hold for both antiferromagnetic and ferromagnetic Kondo lattice. The general exposition is pedagogic in tone.Comment: Review, 258 pages, 19 figure

Applications of GPS Technologies to Field Sports

Global positioning system (GPS) technology was made possible after the invention of the atomic clock. The first suggestion that GPS could be used to assess the physical activity of humans followed some 40 y later. There was a rapid uptake of GPS technology, with the literature concentrating on validation studies and the measurement of steady-state movement. The first attempts were made to validate GPS for field sport applications in 2006. While GPS has been validated for applications for team sports, some doubts continue to exist on the appropriateness of GPS for measuring short high-velocity movements. Thus, GPS has been applied extensively in Australian football, cricket, hockey, rugby union and league, and soccer. There is extensive information on the activity profile of athletes from field sports in the literature stemming from GPS, and this includes total distance covered by players and distance in velocity bands. Global positioning systems have also been applied to detect fatigue in matches, identify periods of most intense play, different activity profiles by position, competition level, and sport. More recent research has integrated GPS data with the physical capacity or fitness test score of athletes, game-specific tasks, or tactical or strategic information. The future of GPS analysis will involve further miniaturization of devices, longer battery life, and integration of other inertial sensor data to more effectively quantify the effort of athletes