Related papers: Quantitatively improved finite-size criteria for s…
Mixed-precision quantization is a promising approach for compressing large language models under tight memory budgets. However, existing mixed-precision methods typically suffer from one of two limitations: they either rely on expensive…
We report on the utility of using Shannons Sampling theorem to solve Quantum Mechanical systems. We show that by extending the logic of Shannons interpolation theorem we can define a Universal Lattice Basis, which has superior interpolating…
We describe quantization schemes for scalar field cosmology in the metric variables with fundamental discreteness imposed with a lattice. The variables chosen for quantization determine the lattice, and each lattice produces distinct…
We present results for the spectrum of b-bbar bound states in the quenched approximation for three different values of the lattice spacing. Results for spin-independent splittings are shown to have good scaling behaviour; spin-dependent…
To understand the finite-size-scaling properties of phases transitions in classical and quantum models in the presence of quenched disorder, it has proven to be fruitful to introduce the notion of a finite-size-pseudo-critical point in each…
In this paper, we consider the optimal design of photonic crystal band structures for two-dimensional square lattices. The mathematical formulation of the band gap optimization problem leads to an infinite-dimensional Hermitian eigenvalue…
The principles of scale setting in lattice QCD as well as the advantages and disadvantages of various commonly used scales are discussed. After listing criteria for good scales, I concentrate on the main presently used ones with an emphasis…
Progress on the calculation of the spectrum from lattice calculations is reviewed. Particular emphasis is placed on discussing our ability to control possible systematic errors coming from finite volume, and extrapolations in quark mass and…
A binary liquid near its consolute point exhibits critical fluctuations of the local composition; the diverging correlation length has always challenged simulations. The method of choice for the calculation of critical points in the phase…
Finite size scaling is a powerful tool to study the critical properties of systems governed by one relevant operator, assuming all irrelevant operators have scaling dimensions much smaller then zero. This condition is likely not satisfied…
The past few years have seen many interesting theoretical developments in lattice QCD. This talk (which is intended for non-experts) focuses on the problem of non-perturbative renormalization and the question of how precisely the continuum…
Cluster states with higher-dimensional lattices that cannot be physically embedded in three-dimensional space have important theoretical interest in quantum computation and quantum simulation of topologically ordered condensed-matter…
We give an intuitive geometric explanation for the apparent breakdown of standard finite-size scaling in systems with periodic boundaries above the upper critical dimension. The Ising model and self-avoiding walk are simulated on…
The sum-rank metric provides a unifying framework that generalizes both the celebrated Hamming and rank metrics, and has found applications in areas such as network coding, distributed storage, and space-time coding. A central problem is to…
We consider the problem of detecting change-points in univariate time series by fitting a continuous piecewise linear signal using the residual sum of squares. Values of the inferred signal at slope breaks are restricted to a finite set of…
We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…
Fine-tuning criteria are frequently used to place upper limits on the masses of superpartners in supersymmetric extensions of the standard model. However, commonly used prescriptions for quantifying naturalness have some important…
I review recent results for heavy-heavy spectroscopy using Lattice NRQCD. The NRQCD collaboration reports that spin-independent splittings for the $\Upsilon$ are scaling for a sensible range of $\beta$ values in the quenched approximation.…
Quantum scale estimation, as introduced and explored here, establishes the most precise framework for the estimation of scale parameters that is allowed by the laws of quantum mechanics. This addresses an important gap in quantum metrology,…
We prove that uniformly small short-range perturbations do not close the bulk gap above the ground state of frustration-free quantum spin systems that satisfy a standard local topological quantum order condition. In contrast with earlier…