Gauge invariance, background fields and modified Ward identities

In this talk the gauge symmetry for Wilsonian flows in pure Yang-Mills theories is discussed. The background field formalism is used for the construction of a gauge invariant effective action. The symmetries of the effective action under gauge transformations for both the gauge field and the auxiliary background field are separately evaluated. Modified Ward-Takahashi and background field identities are used in my study. Finally it is shown how the symmetry properties of the full theory are restored in the limit where the cut-off is removed.Comment: 6 pages, to appear in the Proceedings of the 2nd Conference on the Exact Renormalization Group, Rome 200

Confinement of two-dimensional excitons in a non-homogeneous magnetic field

The effective Hamiltonian describing the motion of an exciton in an external non-homogeneous magnetic field is derived. The magnetic field plays the role of an effective potential for the exciton motion, results into an increment of the exciton mass and modifies the exciton kinetic energy operator. In contrast to the homogeneous field case, the exciton in a non-homogeneous magnetic field can also be trapped in the low field region and the field gradient increases the exciton confinement. The trapping energy and wave function of the exciton in a GaAs two-dimensional electron gas for specific circular magnetic field configurations are calculated. The results show than excitons can be trapped by non-homogeneous magnetic fields, and that the trapping energy is strongly correlated with the shape and strength of the non-homogeneous magnetic field profile.Comment: 9 pages, 12 figure

Domain wall description of superconductivity

In the present work we shall address the issue of electrical conductivity in superconductors in the perspective of superconducting domain wall solutions in the realm of field theory. We take our set up made out of a dynamical complex scalar field coupled to gauge field to be responsible for superconductivity and an extra scalar real field that plays the role of superconducting domain walls. The temperature of the system is interpreted through the fact that the soliton following accelerating orbits is a Rindler observer experiencing a thermal bath.Comment: 9 pages, 5 figures, Latex. Version to appear in PL

Solving non-perturbative flow equations

Non-perturbative exact flow equations describe the scale dependence of the effective average action. We present a numerical solution for an approximate form of the flow equation for the potential in a three-dimensional N-component scalar field theory. The critical behaviour, with associated critical exponents, can be inferred with good accuracy.Comment: Latex, 14 pages, 2 uuencoded figure

Exciton trapping in magnetic wire structures

The lateral magnetic confinement of quasi two-dimensional excitons into wire like structures is studied. Spin effects are take into account and two different magnetic field profiles are considered, which experimentally can be created by the deposition of a ferromagnetic stripe on a semiconductor quantum well with magnetization parallel or perpendicular to the grown direction of the well. We find that it is possible to confine excitons into one-dimensional (1D) traps. We show that the dependence of the confinement energy on the exciton wave vector, which is related to its free direction of motion along the wire direction, is very small. Through the application of a background magnetic field it is possible to move the position of the trapping region towards the edge of the ferromagnetic stripe or even underneath the stripe. The exact position of this 1D exciton channel depends on the strength of the background magnetic field and on the magnetic polarisation direction of the ferromagnetic film.Comment: 10 pages, 7 figures, to be published in J. Phys: Condens. Matte

Device for Determining Variations in Stem Thickness of Trees

In precision agriculture, obtaining accurate information in real-time is essential when making relevant decisions; for example, to determine the hydric stress of plants, continuous monitoring of different plant variables such as stem thickness is required, since this is a very relevant indicator to define the water need. For this purpose, a low-cost prototype was developed to constantly monitor the fluctuations of the diameter of the trunk of a tree. The device has been designed so that it can acquire information autonomously with the help of a control software,. The sensitivity of the device allows measuring variations of up to 8 mm, which is considered optimal for this type of need. During the development of the prototype, the mechanical and electronic structure was designed using simulation software, considering the technical characteristics and functional requirements of the sensor, a control system and power supply. The prototype was built using a 3D printer, the mathematical model used in the control system was validated in a controlled environment presenting a percentage error of 2%, which is considered acceptable, prior to the implementation of the prototype in the field. Keywords: agriculture, water stress, log diameter, 3D model. Resumen En la agricultura de precisión la obtención de información precisa y en tiempo real es fundamental al momento de tomar decisiones relevantes; por ejemplo, para determinar el estrés hídrico de las plantas se requiere de un monitoreo continuo de diferentes variables de la planta como el grosor del tallo puesto que este es un indicador de mucha relevancia para poder definir la necesidad hídrica. Con esta finalidad se desarrolló un prototipo de bajo costo para monitorear constantemente las fluctuaciones del diámetro del tronco de un árbol, el dispositivo ha sido diseñado de manera que pueda adquirir información de forma autónoma apoyado por un software de control, la sensibilidad del dispositivo permite medir variaciones hasta de 8 mm, lo cual se considera óptimo para este tipo de necesidad. Durante el desarrollo del prototipo se diseñó la estructura mecánica y electrónica utilizando software de simulación, tomando en cuenta las características técnicas y requerimientos funcionales del sensor, del sistema de control y alimentación. El prototipo se construyó utilizando una impresora 3D, el modelo matemático utilizado en el sistema de control fue validados en un entorno controlado presentando un error porcentual del 2 %, lo cual se considera aceptable, previo a la implementación del prototipo en campo. Palabras Clave: Agricultura, Estrés hídrico, Diámetro de troco, Modelo 3D

Completeness and consistency of renormalisation group flows

We study different renormalisation group flows for scale dependent effective actions, including exact and proper-time renormalisation group flows. These flows have a simple one loop structure. They differ in their dependence on the full field-dependent propagator, which is linear for exact flows. We investigate the inherent approximations of flows with a non-linear dependence on the propagator. We check explicitly that standard perturbation theory is not reproduced. We explain the origin of the discrepancy by providing links to exact flows both in closed expressions and in given approximations. We show that proper-time flows are approximations to Callan-Symanzik flows. Within a background field formalism, we provide a generalised proper-time flow, which is exact. Implications of these findings are discussed.Comment: 33 pages, 15 figures, revtex, typos corrected, to be published in Phys.Rev.

Self-energy corrections to anisotropic Fermi surfaces

The electron-electron interactions affect the low-energy excitations of an electronic system and induce deformations of the Fermi surface. These effects are especially important in anisotropic materials with strong correlations, such as copper oxides superconductors or ruthenates. Here we analyze the deformations produced by electronic correlations in the Fermi surface of anisotropic two-dimensional systems, treating the regular and singular regions of the Fermi surface on the same footing. Simple analytical expressions are obtained for the corrections, based on local features of the Fermi surface. It is shown that, even for weak local interactions, the behavior of the self-energy is non trivial, showing a momentum dependence and a self-consistent interplay with the Fermi surface topology. Results are compared to experimental observations and to other theoretical results.Comment: 13 pages, 10 figure

Data polygamy : the many-many relationships among urban spatio-temporal data sets

The increasing ability to collect data from urban environments, coupled with a push towards openness by governments, has resulted in the availability of numerous spatio-temporal data sets covering diverse aspects of a city. Discovering relationships between these data sets can produce new insights by enabling domain experts to not only test but also generate hypotheses. However, discovering these relationships is difficult. First, a relationship between two data sets may occur only at certain locations and/or time periods. Second, the sheer number and size of the data sets, coupled with the diverse spatial and temporal scales at which the data is available, presents computational challenges on all fronts, from indexing and querying to analyzing them. Finally, it is nontrivial to differentiate between meaningful and spurious relationships. To address these challenges, we propose Data Polygamy, a scalable topology-based framework that allows users to query for statistically significant relationships between spatio-temporal data sets. We have performed an experimental evaluation using over 300 spatial-temporal urban data sets which shows that our approach is scalable and effective at identifying interesting relationships