Related papers: Discretisation Errors in Landau Gauge on the Latti…
While shrinkage is essential in high-dimensional settings, its use for low-dimensional regression-based prediction has been debated. It reduces variance, often leading to improved prediction accuracy. However, it also inevitably introduces…
We propose an implementation of a two-dimensional $\mathbb{Z}_2$ lattice gauge theory model on a shallow quantum circuit, involving a number of single and two-qubits gates comparable to what can be achieved with present-day and near-future…
Latitude on the choice of initialisation is a shared feature between one-step extended state-space and multi-step methods. The paper focuses on lattice Boltzmann schemes, which can be interpreted as examples of both previous categories of…
We introduce a lattice random walk discretisation scheme for stochastic differential equations (SDEs) that samples binary or ternary increments at each step, suppressing complex drift and diffusion computations to simple 1 or 2 bit random…
We illustrate preliminary results on the gluon propagator computed in generic covariant lattice gauges in the quenched approximation with the Wilson action. We have applied a recently proposed procedure to fix a generic covariant gauge on…
Lattice results for the gluon propagator in SU(2) pure gauge theory obtained on large lattices are presented. Simulated annealing is used throughout to fix the Landau gauge. We concentrate on checks for Gribov copy effects and for scaling…
We discuss the notion of a large field cutoff for lattice gauge models with compact groups. We propose and compare gauge invariant and gauge dependent (in the Landau gauge) criteria to sort the configurations into ``large-field'' and…
Gauge fixing may be done in different ways. We show that using the chain structure to describe a constrained system, enables us to use either a perfect gauge, in which all gauged degrees of freedom are determined; or an imperfect gauge, in…
Controlled Lagrangian and matching techniques are developed for the stabilization of relative equilibria and equilibria of discrete mechanical systems with symmetry as well as broken symmetry. Interesting new phenomena arise in the…
Some basic concepts are discussed to derive renormalisation factors of local lattice operators relevant to deep inelastic structure functions and to other measurable quantities. These $Z$ factors can be used to relate matrix elements…
A multiscale optimization framework for problems over a space of Lipschitz continuous functions is developed. The method solves a coarse-grid discretization followed by linear interpolation to warm-start project gradient descent on…
In this proceeding contribution we discuss how to define canonical momenta for SU(N) lattice gauge theories in the Hamiltonian formalism in a basis where the gauge field operators are diagonal. For an explicit discretisation of SU(2) we…
We address the lattice computation of the gluon propagator in the center-symmetric Landau gauge. After discussing a proper lattice implementation of the center-symmetric Landau gauge, we compare the lattice data with analytical results, and…
Consequences of different discretizations of the two-dimensional Dirac operator on low energy properties (e.g., the number of nodes) and their relations to gauge properties are discussed. Breaking of the gauge invariance was suggested in a…
We compute logarithmic corrections to the O(a^2) lattice artifacts for a class of lattice actions for the non-linear O(n) sigma-model in two dimensions. The generic leading artifacts are of the form $a^2[\ln(a^2)]^{(n/(n-2))}$. We also…
A crucial step in extracting physical predictions from lattice QCD simulations is the scale setting, i.e. the determination of the lattice spacing ($a$) in physical units. Herein, the relative scale setting for different $\beta$'s is…
A generalized gauge fixing which interpolates among the Landau, Coulomb and maximal Abelian gauges is constructed.
In this paper we investigate a priori error estimates for the space-time Galerkin finite element discretization of an optimal control problem governed by a simplified linear gradient enhanced damage model. The model equations are of a…
We introduce a variation of direct maximal center gauge fixing: the "direct Laplacian" center gauge. The new procedure consists of first fixing to the Laplacian adjoint Landau gauge, followed by overrelaxation to the nearby Gribov copy of…
We consider the gluon propagator $D(p^2)$ at various lattice sizes and spacings in the case of pure SU(3) Yang-Mills gauge theories using the Landau gauge fixing. We discuss a class of fits in the infrared region in order to (in)validate…