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Rare-earth (RE) based compounds and alloys are of great interest both for their fundamental physical properties and for applications. In order to tailor the required compounds for a specific task, one must be able to predict the energy…

In this article, we set up a functional setting for mean-field electronic structure models of Hartree-Fock or Kohn-Sham types for disordered crystals. The electrons are quantum particles and the nuclei are classical point-like articles…

The canonical front form Hamiltonian for non-Abelian SU(N) gauge theory in 3+1 dimensions is mapped on an effective Hamiltonian which acts only in the Fock space of one quark and one antiquark. The approach is non-perturbative and exact. It…

Partial differential equations (PDEs) are central to computational electromagnetics (CEM) and photonic design, but classical solvers face high costs for large or complex structures. Quantum Hamiltonian simulation provides a framework to…

We derive an effective Hamiltonian for the two-dimensional Hubbard-Holstein model in the regimes of strong electron-electron and strong electron-phonon interactions by using a nonperturbative approach. In the parameter region where the…

An explicit high-order noncanonical symplectic algorithm for ideal two-fluid systems is developed. The fluid is discretized as particles in the Lagrangian description, while the electromagnetic fields and internal energy are treated as…

We defend the Fock-space Hamiltonian truncation method, which allows to calculate numerically the spectrum of strongly coupled quantum field theories, by putting them in a finite volume and imposing a UV cutoff. The accuracy of the method…

In this thesis we investigate aspects of two problems. In the first part of this thesis, we concentrate on renormalization group methods in Hamiltonian framework. We show that the well-known coupled-cluster many-body theory techniques can…

The electroporoelasticity model, which couples Maxwell's equations with Biot's equations, plays a critical role in applications such as water conservancy exploration, earthquake early warning, and various other fields. This work focuses on…

We propose a numerical method for convection-diffusion problems under low regularity assumptions. We derive the method and analyze it using the primal-dual weak Galerkin (PDWG) finite element framework. The Euler-Lagrange formulation…

A model for crystal field triplet ground states on rare earth or actinide ions with dipolar and quadrupolar couplings to conduction electrons is studied for the first time with renormalization group methods. The quadrupolar coupling leads…

We present a covariant multisymplectic formulation for the Einstein-Hilbert model of General Relativity. As it is described by a second-order singular Lagrangian, this is a gauge field theory with constraints. The use of the unified…

We present results of an ab-initio study of the electronic structure of 140 rare earth compounds. Specifically we predict an electronic phase diagram of the entire range of rare earth monopnictides and monochalcogenides, composed of…

We use neutron scattering and bulk property measurements to determine the single-ion crystal-field Hamiltonians of delafossites $\rm KErSe_2$ and $\rm CsErSe_2$. These two systems contains planar equilateral triangular Er lattices arranged…

We develop a computational method based on an Eulerian field called the "reference map", which relates the current location of a material point to its initial. The reference map can be discretized to permit finite-difference simulation of…

We present a general theory to treat periodic solids with quantum-chemistry methods. It relies on two main developments: 1) the modeling of a solid as a Clifford torus which is a torus that is both periodic and flat and 2) the introduction…

In this paper a hybridized weak Galerkin (HWG) finite element method for solving the Stokes equations in the primary velocity-pressure formulation is introduced. The WG method uses weak functions and their weak derivatives which are defined…

Within the quark model and hyperspherical method, the bound states of four heavy quarks and antiquarks (tetraquarks) are investigated. In hyperradial approximation, the Schroedinger equation is reduced to a one-dimensional equation after…

We propose a new numerical method to solve the Cahn-Hilliard equation coupled with non-linear wetting boundary conditions. We show that the method is mass-conservative and that the discrete solution satisfies a discrete energy law similar…

The three-flavour Wess-Zumino model coupled to electromagnetism is treated as a constraint system using the Faddeev-Jackiw method. Expanding into series of powers of the Goldstone boson fields and keeping terms up to second and third order…