Related papers: Improved superposition schemes for approximate mul…
We extend the method of matrix partition to obtain explicitly the gauge field for noncommutative ADHM construction in some general cases. As an application of this method we apply it to the U(2) 2-instanton and get explicit result for the…
We report a new implementation of multireference algebraic diagrammatic construction theory (MR-ADC) for simulations of electron attachment and ionization in strongly correlated molecular systems (EA/IP-MR-ADC). Following our recent work on…
We report results of autocorrelation measurements in pure $SU(3)$ lattice gauge theory. The computations are performed on the {\sc convex spp1200} parallel platform within the {\sc canopy} programming environment. The focus of our analysis…
Instanton theory is an established method to calculate rate constants of chemical reactions including atom tunneling. Technical and methodological improvements increased its applicability. Still, a large number of energy and gradient…
In this paper, I develop the Soldering formalism in a new domain - the noncommutative planar field theories. The Soldering mechanism fuses two distinct theories showing opposite or complimentary properties of some symmetry, taking into…
We propose new measures of localization and cooperativity for the analysis of atomic rearrangements. We show that for both clusters and bulk material cooperative rearrangements usually have significantly lower barriers than uncooperative…
Local convergence analysis of the augmented Lagrangian method (ALM) is established for a large class of composite optimization problems with nonunique Lagrange multipliers under a second-order sufficient condition. We present a new…
We provide an extended lattice study of the SU(2) gauge theory coupled to one Dirac fermion flavour ($N_{\mathrm{f}} =1$) transforming in the adjoint representation as the continuum limit is approached. This investigation is supplemented by…
This work studies the linear convergence of an accelerated scheme of the Alternating Direction Method of Multipliers (ADMM) for strongly convex and Lipschitz-smooth problems. We use the methodology of expressing the accelerated ADMM as a…
We develop a cooling method controlled by a physical cooling radius that defines a scale below which fluctuations are smoothed out while leaving physics unchanged at all larger scales. We apply this method to study topological properties of…
This dissertation explores block decomposable methods for large-scale optimization problems. It focuses on alternating direction method of multipliers (ADMM) schemes and block coordinate descent (BCD) methods. Specifically, it introduces a…
We present a Monte Carlo Renormalisation Group (MCRG) study of the SU(2) gauge theory with two Dirac fermions in the adjoint representation. Using the two-lattice matching technique we measure the running of the coupling and the anomalous…
By cooling of equilibrium lattice fields at finite temperature in SU(2) gauge theory it has been shown that topological objects (calorons) observed on the lattice in the confined phase possess a dyonic substructure which becomes visible…
In a pilot study, we use the topological charge density defined by the eigenmodes of the overlap Dirac operator (with ultraviolet filtering by mode-truncation) to search for lumps of topological charge in SU(2) pure gauge theory. Augmenting…
Collocation boundary element methods for integral equations are easier to implement than Galerkin methods because the elements of the discretization matrix are given by lower-dimensional integrals. For that same reason, the matrix assembly…
We present a robust, ab initio method for addressing atom-light interactions and apply it to photoionization of argon. We use a close-coupling ansatz constructed on a multi-configurational Hartree-Fock description of localized states and…
We introduce the first bold diagrammatic Monte Carlo approach to deal with polaron problems at finite density non-perturbatively, i.e., by including vertex corrections to high orders. Using Holstein model on a square lattice as a…
The purpose of this paper is to study the influence of relaxation and acceleration techniques on the convergence behavior of the non-overlapping Schwarz algorithm with alternating Dirichlet-Neumann transmission conditions in the context of…
In this paper, two kinds of high-order compact finite difference schemes for second-order derivative are developed. Then a second-order numerical scheme for Riemann-Liouvile derivative is established based on fractional center difference…
We propose a multiconfigurational hybrid density-functional theory which rigorously combines a multiconfiguration self-consistent-field calculation with a density-functional approximation based on a linear decomposition of the…