Charge density and electric charge in quantum electrodynamics

The convergence of integrals over charge densities is discussed in relation with the problem of electric charge and (non-local) charged states in Quantum Electrodynamics (QED). Delicate, but physically relevant, mathematical points like the domain dependence of local charges as quadratic forms and the time smearing needed for strong convergence of integrals of charge densities are analyzed. The results are applied to QED and the choice of time smearing is shown to be crucial for the removal of vacuum polarization effects responible for the time dependence of the charge (Swieca phenomenon). The possibility of constructing physical charged states in the Feynman-Gupta-Bleuler gauge as limits of local states vectors is discussed, compatibly with the vanishing of the Gauss charge on local states. A modification by a gauge term of the Dirac exponential factor which yields the physical Coulomb fields from the Feynman-Gupta-Bleuler fields is shown to remove the infrared divergence of scalar products of local and physical charged states, allowing for a construction of physical charged fields with well defined correlation functions with local fields

Extended Edge States in Finite Hall Systems

We study edge states of a random Schroedinger operator for an electron submitted to a magnetic field in a finite macroscopic two dimensional system of linear dimensions equal to L. The y direction is L-periodic and in the x direction the electron is confined by two smoothly increasing parallel boundary potentials. We prove that, with large probability, for an energy range in the first spectral gap of the bulk Hamiltonian, the spectrum of the full Hamiltonian consists only on two sets of eigenenergies whose eigenfuntions have average velocities which are strictly positive/negative, uniformly with respect to the size of the system. Our result gives a well defined meaning to the notion of edge states for a finite cylinder with two boundaries, and extends previous studies on systems with only one boundary.Comment: 24 pages, 1 figure; Submitte

A two-frequency acousto-optic modulator driver to improve the beam pointing stability during intensity ramps

We report on a scheme to improve the pointing stability of the first order beam diffracted by an acousto-optic modulator (AOM). Due to thermal effects inside the crystal, the angular position of the beam can change by as much as 1 mrad when the radio-frequency power in the AOM is reduced to decrease the first order beam intensity. This is done for example to perform forced evaporative cooling in ultracold atom experiments using far-off-resonant optical traps. We solve this problem by driving the AOM with two radio-frequencies $f_1$ and $f_2$. The power of $f_2$ is adjusted relative to the power of $f_1$ to keep the total power constant. Using this, the beam displacement is decreased by a factor of twenty. The method is simple to implement in existing experimental setups, without any modification of the optics

Exact duality transformations for sigma models and gauge theories

We present an exact duality transformation in the framework of Statistical Mechanics for various lattice models with non-Abelian global or local symmetries. The transformation applies to sigma models with variables in a compact Lie group G with global GxG-symmetry (the chiral model) and with variables in coset spaces G/H and a global G-symmetry (for example, the non-linear O(N) or RP^N models) in any dimension d>=1. It is also available for lattice gauge theories with local gauge symmetry in dimensions d>=2 and for the models obtained from minimally coupling a sigma model of the type mentioned above to a gauge theory. The duality transformation maps the strong coupling regime of the original model to the weak coupling regime of the dual model. Transformations are available for the partition function, for expectation values of fundamental variables (correlators and generalized Wilson loops) and for expectation values in the dual model which correspond in the original formulation to certain ratios of partition functions (free energies of dislocations, vortices or monopoles). Whereas the original models are formulated in terms of compact Lie groups G and H, coset spaces G/H and integrals over them, the configurations of the dual model are given in terms of representations and intertwiners of G. They are spin networks and spin foams. The partition function of the dual model describes the group theoretic aspects of the strong coupling expansion in a closed form.Comment: 57 pages, 15 figures, LaTeX; v2: references update

Search for pair-produced resonances decaying to quark pairs in proton-proton collisions at root s=13 TeV

A general search for the pair production of resonances, each decaying to two quarks, is reported. The search is conducted separately for heavier resonances (masses above 400 GeV), where each of the four final-state quarks generates a hadronic jet resulting in a four-jet signature, and for lighter resonances (masses between 80 and 400 GeV), where the pair of quarks from each resonance is collimated and reconstructed as a single jet resulting in a two-jet signature. In addition, a b-tagged selection is applied to target resonances with a bottom quark in the final state. The analysis uses data collected with the CMS detector at the CERN LHC, corresponding to an integrated luminosity of 35.9 fb(-1), from proton-proton collisions at a center-of-mass energy of 13 TeV. The mass spectra are analyzed for the presence of new resonances, and are found to be consistent with standard model expectations. The results are interpreted in the framework of R-parity-violating supersymmetry assuming the pair production of scalar top quarks decaying via the hadronic coupling lambda ''(312) or lambda ''(323) and upper limits on the cross section as a function of the top squark mass are set. These results probe a wider range of masses than previously explored at the LHC, and extend the top squark mass limits in the (t) over tilde -> qq' scenario.Peer reviewe

Strongly interacting two-dimensional Fermi gas

This thesis is not available on this repository until the author agrees to make it public. If you are the author of this thesis and would like to make your work openly available, please contact us: [email protected] Library can supply a digital copy for private research purposes; interested parties should submit the request form here: http://www.lib.cam.ac.uk/collections/departments/digital-content-unit/ordering-imagesPlease note that print copies of theses may be available for consultation in the Cambridge University Library's Manuscript reading room. Admission details are at http://www.lib.cam.ac.uk/collections/departments/manuscripts-university-archive

Contrôle spatio-temporel de la génération d'harmoniques dans les semiconducteurs pour l'émission d'impulsions attosecondes

La génération d'harmoniques d'ordre élevées dans les milieux condensés est un domaine émergent depuis sa première observation en 2011. La forte dépendance des harmoniques à la structure de bande cristalline et aux paramètres laser en fait une excellente observable des mécanismes fondamentaux de génération. De plus, la configuration compacte de la source combinée à la possibilité de structurer le milieu de génération en fait une source prometteuse de rayonnement extrême ultraviolet pour, par exemple, des applications de spectroscopie ou d'imagerie. Dans cette thèse, nous étudions trois caractéristiques de la génération d'harmoniques dans les cristaux. Premièrement, l'effet des changements de structure de bande induits par le dopage sur le processus d'émission. Les deux exemples de systèmes sont l'oxyde de magnésium dopé au chrome et le silicium implanté au gallium, pour lesquels le dopage conduit à une amélioration du rendement de génération. Ensuite, nous montrons qu'en utilisant une technique d'imagerie par diffraction cohérente, il est possible d'imager des nanostructures uniquement en se basant sur les harmoniques émises par la structure elle-même. Parce que la nanostructuration de surface émerge comme un moyen d'induire des propriétés complexes directement dans le faisceau harmonique, comme un moment angulaire orbital, cela ouvre la possibilité d'une caractérisation in-situ de ces structures. Enfin, le concept de porte de polarisation utilisé dans les gaz est adapté pour les solides en utilisant la forte réponse anisotrope des harmoniques. C'est utilisé pour façonner temporellement l'émission et permettre la génération d'impulsions attosecondes isolées.High harmonic generation in condensed media has been an emerging field since its first observation in 2011. The strong dependency of the harmonics on the crystal band structure and laser parameters make them an excellent observable of the fundamental mechanisms of generation. Moreover, the compact configuration of the source combined with the possibility for structuring the generation medium makes it a promising source of extreme ultraviolet radiation for e.g. spectroscopy or imaging applications. In this thesis, we investigate three different aspects of the high harmonic generation in crystals. First, doping that induces changes of the band structure and its effect on the emission process. The two example systems for this are chromium doped magnesium oxide and gallium implanted silicon, for which the doping leads to an enhancement of the harmonic yield. After, we show that by using a coherent diffraction imaging technique, it is possible to image nanostructures solely based on the harmonics emitted by the structure itself. Because surface nanostructuring is emerging as a way of inducing complex properties directly into the harmonic beam, such as an orbital angular momentum, this opens up the possibility of in-situ characterization of these structures. Finally, the concept of polarization gating used in gases is adapted for solids by using the strong anisotropic harmonic response. It is used in order to temporally shape the emission and push towards isolated attosecond pulse generation

Parliamentary Sovereignty, Popular Sovereignty, Formation of Consensus.: Anmerkungen zur englischen Revolution 1640-1649

This paper attempts to delineate the development of constitutional ideas from pre-revolutionary theories of consensus to parliamentary sovereignty and, finally, the challenge of popular sovereignty during the English Revolution 1640-1660. Before 1641, there existed at least a semantic consensus on basic constitutional issues. Both, parliamentary and royalist proclamations praised the ancient constitution as a divinely ordained „mixed monarchy“. However, the use of similar metaphors in constitutional theory did not correspond to harmony in practical politics concerning the constitution. Only after the beginning of the civil war, Henry Parker and others clearly proclaimed parliamentary sovereignty as a theoretical weapon in order to justify the revolutionary changes which had occurred. Later on, however, the Levellers challenged the theory of parliamentary sovereignty as a tactical compromise between „mixed monarchy“ and popular sovereignty.This paper attempts to delineate the development of constitutional ideas from pre-revolutionary theories of consensus to parliamentary sovereignty and, finally, the challenge of popular sovereignty during the English Revolution 1640-1660. Before 1641, there existed at least a semantic consensus on basic constitutional issues. Both, parliamentary and royalist proclamations praised the ancient constitution as a divinely ordained „mixed monarchy“. However, the use of similar metaphors in constitutional theory did not correspond to harmony in practical politics concerning the constitution. Only after the beginning of the civil war, Henry Parker and others clearly proclaimed parliamentary sovereignty as a theoretical weapon in order to justify the revolutionary changes which had occurred. Later on, however, the Levellers challenged the theory of parliamentary sovereignty as a tactical compromise between „mixed monarchy“ and popular sovereignty

Blumen-Träume - Salonstück, Op. 5

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