Line Defects and Radiation in N=2 Conformal Theories

We study the conformal data of a generic superconformal line defect preserving half of the supercharges in a four-dimensional N = 2 conformal theory. We prove a theory independent relation between the one-point function of the stress tensor in the presence of the line defect and the two-point function of the displacement operator. When the defect is interpreted as a heavy charged particle in a gauge theory, the result relates the energy emitted through bremsstrahlung with the coupling of the stress tensor to the particle at rest.

Topological defects and gravity in theories with extra dimensions

Ewald Rössl

Recent proposals of large and infinite extra dimensions triggered a strong research activity in theories in which our universe is considered as a sub-manifold of some higher-dimensional space-time, a so-called 3-brane. In this context, it is generally assumed that some mechanism is at work which binds Standard Model particles to the 3-brane, an effect often referred to as the localization of matter on the brane. Gravity, however, is allowed to propagate in general also in the extra dimensions. As demonstrated by Randall and Sundrum in 1999, it is also possible to localize gravity itself on a 3-brane. In the setup they proposed. the 3-brane is realized as a singular domain wall separating two patches of 3-dimensional anti-de-Sitter (AdS5) space-time. The potential between two test masses on the brane at distances larger than the AdS5-radius was shown to be the usual 4-dimensional Newtonian 1/r potential with strongly suppressed corrections. The model of Randall and Sundrum, usually referred to as the Randall-Sundrum II setup, constitutes the center of interest for this thesis. The main goal of this work is to find possible generalizations to higher dimensions of the simple setup considered by Randall and Sundrum. One of the motivations for such a generalization is that a realistic theory should possibly be able to explain the chiral nature of 4-dimensional fermions on the brane. One way to explain chiral fermions from higher dimensions is to consider 3-braves identified with the cores of topological defects located in a higher-dimensional transverse space. Naturally a richer topological structure of the field configuration in transverse space provides the possibility of a more realistic spectrum of chiral fermions localized on the 3-brane. After two introductory chapters on extra dimensions and non-factorizable geometries which are relevant for the Randall-Sundrum II model, we briefly discuss basics of topological defects in the following third chapter. In the rest of the third chapter we consider various solutions to higher-dimensional Einstein equations coupled to a series of physically different sources and discuss their properties of localization of gravity. Due to their asymptotic nature, these solutions are only valid far from the cores of the defects in transverse space. Therefore, it seems reasonable to complement the consideration by presenting a particular numerical example of a solution to the Einstein equations coupled to a set of scalar and gauge fields: this solution describes a 3-brave realized as a 't Hooft-Polyakov monopole residing in the 3-dimensional transverse space of a 7-dimensional space-time. The last chapter of this work is dedicated to the study of a modification of the original Randall-Sundrum II model of another kind. The motivation is given by the geodesic incompleteness of the latter scenario with respect to time-like and light-like geodesics. We will describe a model which resembles the Randall-Sundrurn II model with respect to its properties of gravity localization but with the advantage that the underlying space-time manifold is geodesically complete. Parts of the calculations related to the properties of gravity at low energies in this model are rather technical in nature and we therefore preferred to assemble them in several appendices. We finally add some concluding remarks and discuss possible further developments.

EPFL2004

Aspects of two dimensional magnetic Schrödinger operatorsquantum hall systems and magnetic Stark resonances

Christian Ferrari

In this PhD thesis we deal with two mathematical problems arising from quantum mechanics. We consider a spinless non relativistic quantum particle whose configuration space is a two dimensional surface S. We also suppose that the particle feels the effect of an homogeneous magnetic field perpendicular to the surface S. In the first case S = R × SL1, the infinite cylinder of circumference L, corresponding to periodic boundary conditions, while in the second one S = R2. In both cases the particle feels the effect of an additional suitable potential. We are thus left with the study of two specific classes of Schrödinger operators. The operator of the first class generates the dynamics of the particle when it is submitted to an Anderson-type random potential, as well as to a non random potential confining the particle along the cylinder axis in an interval of length L. In this case we describe the spectrum and classify it by the quantum mechanical current carried by the corresponding eigenfunctions. We prove that there are spectral regions in which all the eigenvalues have an order one current with respect to L, and spectral regions where eigenvalues with order one current and eigenvalues with infinitesimal current with respect to L are intermixed. These results are relevant for the theory of the integer quantum Hall effect. The second Schrödinger operator class corresponds to the physical situation where the potential is the sum of a "local" potential and of a potential due to a weak constant electric field F. In this case we show that the resonant states, induced by the electric field, decay exponentially at a rate given by the imaginary part of the eigenvalues of some non self-adjoint operator. Moreover we prove an upper bound on this imaginary part that turns out to be of order exp(-1/F2) as F goes to zero. Therefore the lifetime of the resonant states is at least of order exp(-1/F2).

EPFL2003

Development and validation of data sets and Monte Carlo methods for electron/positron transport at low and medium energies

Cezarina Elena Negreanu

When exposed to ionising radiation, living tissue can potentially suffer somatic and genetic damage - effects depending mainly on the radiation dose or energy absorbed, the type of radiation, and the type and mass of cells affected. It is well known that large doses of radiation lead to high damage of the cell nucleus and additional cell structures, which results in harmful somatic effects, and even rapid death of the individual exposed, while at low doses, cancer is by far the most important possible consequence. Understanding the mechanisms by which low doses of radiation cause cell damage is thus of great significance, not only from this viewpoint but also from that of practical medical physics applications such as radiotherapy treatment planning. Ionising radiation, such as electrons and positrons, begins to cause damage to the genome of a living cell by direct ionisation of atoms, thus depositing energy in the DNA double helix itself. The energy threshold for inducing strand-breaks by electrons, however, is around 7 eV, well below the energy levels required for direct ionization. The low-energy electrons that are set in motion around the tracks of energetic charged particles, for example, are responsible for a multitude of low-energy events (energy transfer of the order of 10 eV), which play a significant role in inducing molecular damage. Assessing the spatial configuration of energy transfer events and the deposited energy spectra, in regions of cellular and sub-cellular dimensions, can be aimed at via the application of appropriate Monte Carlo simulation tools. Such calculations depend primarily on an accurate knowledge of the production and subsequent slowing down of secondary electrons that form the basic structure of the charged particle track. In the above context, an important requirement is the provision of detailed quantitative information concerning the interaction cross sections of electrons over an energy range extending down to low energies, i.e. including the sub-excitation domain. In addition, developing fast particle-transport simulation algorithms to cover the entire slowing down process efficiently is a key aspect. Thus, the present doctoral research has, as global goal, the development and validation of new Monte Carlo calculational tools for electron and positron transport in biological materials, both at high and low energies. More specifically, it aims at providing (i) a comprehensive and accurate set of appropriate cross section data, and (ii) a fast and reliable algorithm for the simulation of charged particle transport. Thus, the first part of the thesis concerns the assessment, further development and validation of standard theoretical models for generating electron and positron cross sections to cover the main interactions of these particles with matter, in particular with the basic atomic components of biomaterials (water, bio-polymers, etc.). This has been done for bremsstrahlung, and both elastic and inelastic scattering, considering a wide range of atomic numbers and high up to thermal incident particle energies. In particular, the excitation cross sections for medium and low energies (down to 1 eV) have been derived by using a new formalism based on many-body field theory. The accuracy of the presently obtained data sets are assessed against other theoretical models, as also a large experimental database for each type of interaction, so that both a comprehensive coverage and adequate accuracies have been ensured for the cross section data sets generated. In the second part of the thesis, an extension of the Monte Carlo code system PENELOPE is first undertaken such that use can be made of elastic scattering differential cross sections which have been made available in numerical form. Thereby, new computational routines (incorporated into the new code PENELAST) prepare the cross sections, needed for a given energy and scattering angle, by applying a fast and accurate sampling technique to a provided data set. The present development will allow various electron and positron cross section data libraries, appropriately formatted, to be used with PENELOPE for benchmarking purposes. The development of a high calculation-speed (Class I) Monte Carlo tool for charged particle transport in biological materials has then been addressed. Thereby, a numerical algorithm for calculating the multiple-scattering angular distributions of high energy electrons and positrons is developed, based on the multiple-scattering theory of Lewis which accounts for energy losses within the continuous slowing down approximation. Partial-wave elastic scattering differential cross sections made available in numerical form, as indicated above, are used for the calculations, the inelastic scattering differential cross sections being obtained from the Sternheimer-Liljequist generalized oscillator strength model implemented in PENELOPE. The new code LEWIS has been used to calculate multiple-scattering angular distributions for given path lengths and can be readily adopted for Class I Monte Carlo simulations. The simultaneous generation of a large number of Legendre expansion coefficients is rendered possible, both rapidly and accurately. Results from LEWIS have been found to be in satisfactory agreement, both with detailed simulations carried out using PENELAST and with various sets of experimental data for high to medium energy electrons. In brief, the present research represents a significant improvement in the quality of Monte Carlo modelling of charged particle slowing down processes, thus contributing to understanding the. role of low-energy secondary electrons in radiation protection studies. It will also allow the further development of a complete Class I Monte Carlo code, which can then be reliably used in practical applications such as radiation treatment planning.

EPFL2005