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A major challenge in creating a quantum computer is to find a quantum system that can be used to implement the qubits. For this purpose, deep centers are prominent candidates, and ab initio calculations are one of the most important tools…
We analyze a system of two colliding ultracold atoms under strong harmonic confinement from the viewpoint of quantum defect theory and formulate a generalized self-consistent method for determining the allowed energies. We also present two…
Many methods for computing electronic correlation effects at finite temperature are related to many-body perturbation theory in the grand-canonical ensemble. In most applications, however, the average number of electrons is known rather…
We investigate the basis-set convergence of electronic correlation energies calculated using coupled cluster theory and a recently proposed finite basis-set correction technique. The correction is applied to atomic and molecular systems and…
In this thesis, we present a novel method combining energy-based finite-size scaling with tensor network renormalization (TNR) to study phase transitions in lattice models. This approach effectively calculates running coupling constants and…
Computer simulations of model systems are widely used to explore striking phenomena in promising applications spanning from physics, chemistry, biology, to materials science and engineering. The long range electrostatic interactions between…
The charge asymmetry in the differential cross section of high-energy $\mu^+\mu^-$ photoproduction in the electric field of a heavy atom is obtained. This asymmetry arises due to the Coulomb corrections to the amplitude of the process…
Present day electromagnetic field calculations have limitations that are due to techniques employing edge-based discretization methods. While these vector finite element methods solve the issues of tangential continuity of fields and the…
Effective potentials of the relativistic m\alpha^6 order correction for the ground state of the Coulomb two-center problem are calculated. They can be used to evaluate the relativistic contribution of that order to the energies of hydrogen…
We review the use of continuum quantum Monte Carlo (QMC) methods for the calculation of energy gaps from first principles, and present a broad set of excited-state calculations carried out with the variational and fixed-node diffusion QMC…
We derive an approximate expression for a "radiative potential" which can be used to calculate QED strong Coulomb field radiative corrections to energies and electric dipole (E1) transition amplitudes in many-electron atoms with an accuracy…
Periodic supercell models of electric double layers formed at the interface between a charged surface and an electrolyte are subject to serious finite size errors and require certain adjustments in the treatment of the long-range…
We investigate the impact of one-loop radiative corrections in a non-supersymmetric model of hybrid inflation with a chaotic (polynomial-like) potential,$V(\phi) = V_0 + \lambda_p \phi^p$, in the light of the latest constraints from…
Using the Dirac equation, we study corrections to electron binding energies and hyperfine splittings of atomic hydrogen and hydrogen-like ions due to finite nuclear size (FNS) effects, relativistic QED radiative corrections and nuclear…
We present a posteriori error estimates for a recently developed atomistic/continuum coupling method, the Consistent Energy-Based QC Coupling method. The error estimate of the deformation gradient combines a residual estimate and an a…
Layer potentials represent solutions to partial differential equations in an integral equation formulation. When numerically evaluating layer potentials at evaluation points close to the domain boundary, specialized quadrature techniques…
We present an a posteriori error estimate based on equilibrated stress reconstructions for the finite element approximation of a unilateral contact problem with weak enforcement of the contact conditions. We start by proving a guaranteed…
We examine the accuracy of an intrinsically one-dimensional quantum electrodynamics to predict accurately the forces and charges of a three-dimensional system that has a high degree of symmetry and therefore depends effectively only on a…
We introduce and motivate the method of effective chsrges, and consider how to implement an all-orders resummation of large kinematical logarithms in this formalism. Fits for QCD \Lambda and power corrections are performed for the e+e-…
We propose a general approach to reducing basis set incompleteness error in electron correlation energy calculations. The correction is computed alongside the correlation energy in a single calculation by modifying the electron interaction…