Lattice gauge theory | EPFL Graph Search

In physics, lattice gauge theory is the study of gauge theories on a spacetime that has been discretized into a lattice. Gauge theories are important in particle physics, and include the prevailing theories of elementary particles: quantum electrodynamics, quantum chromodynamics (QCD) and particle physics' Standard Model. Non-perturbative gauge theory calculations in continuous spacetime formally involve evaluating an infinite-dimensional path integral, which is computationally intractable. By working on a discrete spacetime, the path integral becomes finite-dimensional, and can be evaluated by stochastic simulation techniques such as the Monte Carlo method. When the size of the lattice is taken infinitely large and its sites infinitesimally close to each other, the continuum gauge theory is recovered. Basics In lattice gauge theory, the spacetime is Wick rotated into Euclidean space and discretized into a lattice with sites separated by distance a and connec

Conceptual Design of a Sustainable Waste Burning Molten Salt Reactor

Boris Aviv Hombourger

For an energy source to qualify as sustainable, it must maximize the efficiency with which it uses natural resources while minimizing the amounts of waste it produces. Currently deployed nuclear power plants however use a very limited amount of the energy contained in natural nuclear fuels such as Uranium and Thorium and produce long-lived nuclear waste that must be dealt with. Molten Salt Reactors (MSRs) are one family of advanced reactors designs with the potential for safe and sustainable energy production due to their use of a liquid molten salt fuel. This thesis aimed at reviewing MSR designs that have been proposed in the past, investigating alternative design possibilities and proposing a concept capable of disposing of existing waste in a sustainable manner. One possibility to do so is to design a reactor to run on an isobreeding closed fuel cycle while using existing actinide waste as a start-up inventory, which is the route investigated in this thesis. For this purpose, the EQL0D fuel cycle procedure was developed using the MATLAB environment and the Serpent 2 Monte Carlo neutron transport code to simulate the start-up, transition and equilibrium of MSRs. The procedure was then applied to investigate the performance at equilibrium of several candidate fuel salts and moderators in an infinite lattice and in a closed Uranium-Plutonium and Thorium-Uranium fuel cycle. The results showed that only an isobreeding closed Uranium-Thorium fuel cycle can be achieved in moderated MSRs, while both isobreeding Uranium-Plutonium and Thorium-Uranium closed fuel cycles can be sustained in fast-spectrum MSRs, which additionally show a substantial reactivity margin that enable them to dispose of poorly fissile nuclides. The transition behavior of selected fluoride- and chloride-fueled reactors was then investigated. The fluoride-fueled cores all feature a closed Thorium-Uranium fuel cycle and included two historical graphite-moderated designs (the single- and two-fluid Molten Salt Breeder Reactors) and a modern fast-spectrum design (Molten Salt Fast Reactor). The chloride-fueled cores were proposed based on the results obtained in the infinite lattice study. The results obtained indicated that the transuranic-burning capabilities of fluoride-fueled reactors are substantially limited by the low solubility of transuranic trifluorides in fluoride salt mixtures, while no such limitation was found in chloride salts. On the other hand, chloride salts necessitate substantially larger cores and inventories. Finally, the possibility of operating MSRs on two types of open cycles without fuel processing, breed-and-burn and once-through, was investigated to alleviate concerns related to the uncertainties related to the technical feasibility of molten salt fuel processing in closed fuel cycles. The results obtained show that it is possible to operate chloride-fueled MSRs in a sustainable breed-and-burn fuel cycle and also on an open cycle with appreciable burn-ups achieved.

EPFL2018

A Framework for Numerical Simulations of Structure Formation

Claude Becker

In the absence of a full analytical treatment of nonlinear structure formation in the universe, numerical simulations provide the critical link between the properties of the underlying model and the features of the observed structures. Currently N-body simulations are the main tool to study structure growth. We explore an alternative framework for numerical simulations of structure formation. The underlying idea is to replace the long-range gravitational force in the Vlasov-Poisson system by a purely local interaction. To this end we trade the classical phase space distribution for its quantum mechanical counterpart, the Wigner distribution function. Its dynamical equation is equivalent to the Schrödinger equation and reduces to the Vlasov equation in the formal semi-classical limit. The proposed framework allows in principle to simulate systems with arbitrary phase space distributions and could for instance be beneficial for simulations of warm dark matter, where the velocity dispersion is important. We discuss several methods to obtain a set of wavefunctions whose Wigner distribution is close to a given initial phase space distribution function. An auxiliary gauge field is introduced to mediate the gravitational interaction, thereby obtaining a local Schrödinger-Maxwell system. We also use the ideas of lattice gauge theories to obtain a fully gauge-invariant discretization of the equations of motion. Their iterative solution was implemented in a three-dimensional simulation code. We discuss its computational complexity and memory requirements. Several testbed simulations were performed with this method. We compared the gravitational collapse of a Gaussian wavefunction with an independent numerical solution of the spherically symmetric Schrödinger-Newton system. The results were found to be in good agreement. Finally, a simple example of the growth of cosmic perturbations is investigated within our framework. We conclude by outlining various possible directions to optimize and develop our method.

EPFL2011

Ising Model: Local Spin Correlations and Conformal Invariance

Clément Hongler, Sung Chul Park

We study the 2-dimensional Ising model at critical temperature on a simply connected subset of the square grid Z2. The scaling limit of the critical Ising model is conjectured to be described by Conformal Field Theory; in particular, there is expected to be a precise correspondence between local lattice fields of the Ising model and the local fields of Conformal Field Theory. Towards the proof of this correspondence, we analyze arbitrary spin pattern probabilities (probabilities of finite spin configurations occurring at the origin), explicitly obtain their infinite-volume limits, and prove their conformal covariance at the first (non-trivial) order. We formulate these probabilities in terms of discrete fermionic observables, enabling the study of their scaling limits. This generalizes results of Hongler (Conformal invariance of Ising model correlations. Ph.D. thesis, [Hon10]), Hongler and Smirnov (Acta Math 211(2):191-225, [HoSm13]), Chelkak, Hongler, and Izyurov (Ann. Math. 181(3), 1087-1138, [CHI15]) to one-point functions of any local spin correlations. We introduce a collection of tools which allow one to exactly and explicitly translate any spin pattern probability (and hence any lattice local field correlation) in terms of discrete complex analysis quantities. The proof requires working with multipoint lattice spinors with monodromy (including construction of explicit formulae in the full plane), and refined analysis near their source points to prove convergence to the appropriate continuous conformally covariant functions.