Quantum electrodynamics | EPFL Graph Search

In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons and represents the quantum counterpart of classical electromagnetism giving a complete account of matter and light interaction. In technical terms, QED can be described as a very accurate way to calculate the probability of the position and movement of particles, even those massless such as photons, and the quantity depending on position (field) of those particles, and described light and matter beyond the wave-particle duality proposed by Einstein in 1905. Richard Feynman called it "the jewel of physics" for its extremely accurate predictions of quantities like the anomalous magnetic moment of the electron and the Lamb shift of the energy levels of hydrogen. History of quantum mechanics and History of quantum field theory The first formulation of a quantum theory describing radiation and matter interaction is attributed to British scientist Paul Dirac, who (during the 1920s) was able to compute the coefficient of spontaneous emission of an atom. Dirac described the quantization of the electromagnetic field as an ensemble of harmonic oscillators with the introduction of the concept of creation and annihilation operators of particles. In the following years, with contributions from Wolfgang Pauli, Eugene Wigner, Pascual Jordan, Werner Heisenberg and an elegant formulation of quantum electrodynamics by Enrico Fermi, physicists came to believe that, in principle, it would be possible to perform any computation for any physical process involving photons and charged particles. However, further studies by Felix Bloch with Arnold Nordsieck, and Victor Weisskopf, in 1937 and 1939, revealed that such computations were reliable only at a first order of perturbation theory, a problem already pointed out by Robert Oppenheimer.

Predictors and predictands of linear response in spatially extended systems

Umberto Maria Tomasini

The goal of response theory, in each of its many statistical mechanical formulations, is to predict the perturbed response of a system from the knowledge of the unperturbed state and of the applied perturbation. A new recent angle on the problem focuses on providing a method to perform predictions of the change in one observable of the system using the change in a second observable as a surrogate for the actual forcing. Such a viewpoint tries to address the very relevant problem of causal links within complex system when only incomplete information is available. We present here a method for quantifying and ranking the predictive ability of observables and use it to investigate the response of a paradigmatic spatially extended system, the Lorenz '96 model. We perturb locally the system and we then study to what extent a given local observable can predict the behaviour of a separate local observable. We show that this approach can reveal insights on the way a signal propagates inside the system. We also show that the procedure becomes more efficient if one considers multiple acting forcings and, correspondingly, multiple observables as predictors of the observable of interest.

SPRINGER HEIDELBERG2021

Asymptotic freedom, Haldane gap and edge states of SU(N) spin chains

Samuel Gozel

In this thesis we study various one-dimensional quantum spin systems with SU(2) and SU(N) symmetry. We investigate the short-distance behavior of the SU(2) Heisenberg model in the limit of large spin and show that there exists an extended regime where perturbation theory, in the form of spin-wave theory, can be successfully applied. The reason for this perturbative regime stems from the asymptotic freedom of the nonlinear sigma model onto which the Heisenberg model can be mapped. When considering observables which respect the rotational invariance of the model, we observe a cancellation of infrared divergences in the perturbative expansions, leading to a meaningful description of correlation functions. We then turn to the study of SU(N) models. Building on the representation theory of the SU(N) group and on the matrix product state (MPS) formalism, we introduce a generic method to construct Affleck-Kennedy-Lieb-Tasaki (AKLT) models having edge states described by any self-conjugate irreducible representation (irrep) of SU(N). A simple example is given by a spin-1 AKLT model having spin-1 edge states. The phase transition between this model and the original AKLT model is shown to be continuous and to correspond to a topological phase transition described by the SU(2) level-1 Wess-Zumino-Witten conformal field theory universality class. In addition we study an SU(3) AKLT model for the 3-box symmetric irrep at each site. We demonstrate that the edge states are adjoint edge irreps, we extract its correlation length and provide a useful construction as an optimal MPS. Finally, we develop a density matrix renormalization group algorithm based on standard Young tableaus and subduction coefficients to make full use of the non-abelian symmetry and to investigate the SU(3) Heisenberg model with 3-box symmetric irrep at each site. We show that the model has a finite gap above the singlet ground state, in agreement with an extension of the Haldane conjecture to SU(3) chains in the fully symmetric irreps. We also argue that there are five branches of elementary excitations living in four different irreps, each of which is gapped.

EPFL2020

Systematic Sensitivity and Uncertainty Analysis of Sodium-Cooled Fast Reactor Systems

Friederike Bostelmann

Sodium-cooled fast reactor (SFR) technologies have the potential to guarantee energy supply and to reduce the burden of nuclear waste for future generations. For an adequate simulation of these reactor systems, well-established tools that have so far been applied mainly to light water reactor (LWR) concepts need to be validated and enhanced. For licensing purposes, there is an increasing interest in replacing conservative calculations by best-estimate calculations supplemented by uncertainty analyses. Nuclear data are a major source of uncertainties in reactor physics calculations. The propagation of nuclear data uncertainties to important system responses is important for determining appropriate safety margins in safety analyses. A systematic approach for quantifying nuclear data--induced uncertainties for all stages of modeling is needed to assess the performance of traditional methods for uncertainty and sensitivity analysis and to unveil the major drivers of observed uncertainties in SFRs. This thesis presents a basis for such a systematic approach through the use of sub-exercises that address different levels of modeling as addition to the OECD/NEA Benchmark for Uncertainty Analysis in Modelling of SFRs. The major analysis method applied within this thesis was the random sampling--based XSUSA method in which nuclear data is varied based on the corresponding covariance data. As a basis for analyses using several multigroup neutron transport codes from the SCALE code system, new multigroup cross section and covariance libraries were developed and optimized for the analysis of SFR systems. In order to use the time-efficient XSUSA method in combination with the SCALE 6.2 release, SCALE's random sampling sequence Sampler was extended to allow the perturbation of cross sections after the self-shielding calculation, including an optional approximation for consideration of implicit effects. XSUSA allowed for the determination of one correlation-based sensitivity index to identify the main contributors to observed uncertainties. This sensitivity analysis was extended by a second correlation-based sensitivity index, as well as variance-based Sobol' sensitivity indices. Furthermore, corresponding indices that use sensitivity coefficients from perturbation theory were developed to allow for comparisons between the various approaches. Finally, systematic uncertainty and sensitivity analyses with respect to nuclear data were performed based on the developed specifications and the described developments. It was found that the analysis of simple models is sufficient for initial assessments of the impact of nuclear data uncertainties on larger scale models as well as the corresponding identification of the uncertainties' major drivers. In general, significantly larger uncertainties for eigenvalues and reactivity coefficients were observed than in corresponding LWR calculations. The main contributor to the uncertainty for most output quantities was identified as inelastic scattering of U-238. Other relevant contributors are the scattering reactions of the coolant and the structural material. By comparing results based on various methods and models, the studies presented in this thesis contribute to the development and assessment of calculation methods and models for uncertainty analysis accompanying best-estimate reactor simulations of SFR.

EPFL2020

Asymptotic freedom, Haldane gap and edge states of SU(N) spin chains

Samuel Gozel

EPFL2020

Systematic Sensitivity and Uncertainty Analysis of Sodium-Cooled Fast Reactor Systems

Friederike Bostelmann

EPFL2020