Color screening in 2+12+1 flavor QCD at large distances

We study correlation functions of spatially separated static quark-antiquark pairs in $2+1$ flavor QCD in order to investigate the nature of color screening at high temperatures. We perform lattice calculations in a wide temperature range, $116~\text{MeV} \leq T \leq 5814~\text{MeV}$, using the highly improved staggered quark (HISQ) action and several lattice spacings to control discretization effects. We alleviate the UV noise problem through the use of four dimensional hypercubic (HYP) smearing, which enables the reconstruction of correlators and determination of screening properties even at low temperatures and at large distances.Comment: 8 pages, 9 figure

QuantumFDTD - A computational framework for the relativistic Schrödinger equation

We extend the publicly available quantumfdtd code. It was originally intended for solving the time-independent three-dimensional Schrödinger equation via the finite-difference time-domain (FDTD) method and for extracting the ground, first, and second excited states. We (a) include the case of the relativistic Schrödinger equation and (b) add two optimized FFT-based kinetic energy terms for the non-relativistic case. All the three new kinetic terms are computed using Fast Fourier Transform (FFT).We release the resulting code as version 3 of quantumfdtd. Finally, the code now supports arbitrary external filebased potentials and the option to project out distinct parity eigenstates from the solutions. Our goal is quark models used for phenomenological descriptions of QCD bound states, described by the three-dimensional Schrödinger equation. However, we target any field where solving either the non-relativistic or the relativistic three-dimensional Schrödinger equation is required

Charm mass effects in the static energy computed in 2+1+1 flavor lattice QCD

We report our analysis for the static energy in (2+1+1)-flavor QCD over a wide range of lattice spacings and several quark masses. We obtain results for the static energy out to distances of nearly 1 fm, allowing us to perform a simultaneous determination of the lattice scales $r_2$, $r_1$ and $r_0$ as well as the string tension, $\sigma$. While our results for ${r_0}/{r_1}$ and $r_0$ $\sqrt{\sigma}$ agree with published (2+1)-flavor results, our result for ${r_1}/{r_2}$ differs significantly from the value obtained in the (2+1)-flavor case, likely due to the effect of the charm quark. We study in detail the effect of the charm quark on the static energy by comparing our results on the finest lattices with the previously published (2+1)-flavor QCD results at similar lattice spacing. The lattice results agree well with the two-loop perturbative expression of the static energy incorporating finite charm mass effects.Comment: 9 pages, 4 figures, The 39th International Symposium on Lattice Field Theory (Lattice2022),8-13 August, 2022,Bonn, German

QuantumFDTD - A computational framework for the relativistic Schrödinger equation

We extend the publicly available quantumfdtd code. It was originally intended for solving the time-independent three-dimensional Schrödinger equation via the finite-difference time-domain (FDTD) method and for extracting the ground, first, and second excited states. We (a) include the case of the relativistic Schrödinger equation and (b) add two optimized FFT-based kinetic energy terms for the non-relativistic case. All the three new kinetic terms are computed using Fast Fourier Transform (FFT).We release the resulting code as version 3 of quantumfdtd. Finally, the code now supports arbitrary external filebased potentials and the option to project out distinct parity eigenstates from the solutions. Our goal is quark models used for phenomenological descriptions of QCD bound states, described by the three-dimensional Schrödinger equation. However, we target any field where solving either the non-relativistic or the relativistic three-dimensional Schrödinger equation is required

Static Energy in (2+1+12+1+1)-Flavor Lattice QCD: Scale Setting and Charm Effects

We present results for the static energy in ($2+1+1$)-flavor QCD over a wide range of lattice spacings and several quark masses, including the physical quark mass, with ensembles of lattice-gauge-field configurations made available by the MILC Collaboration. We obtain results for the static energy out to distances of nearly $1$~fm, allowing us to perform a simultaneous determination of the scales $r_{1}$ and $r_{0}$ as well as the string tension, $\sigma$. For the smallest three lattice spacings we also determine the scale $r_{2}$. Our results for $r_{0}/r_{1}$ and $r_{0}\sqrt{\sigma}$ agree with published ($2+1$)-flavor results. However, our result for $r_{1}/r_{2}$ differs significantly from the value obtained in the ($2+1$)-flavor case, which is most likely due to the effect of the charm quark. We also report results for $r_{0}$, $r_{1}$, and $r_{2}$ in~fm, with the former two being slightly lower than published ($2+1$)-flavor results. We study in detail the effect of the charm quark on the static energy by comparing our results on the finest two lattices with the previously published ($2+1$)-flavor QCD results at similar lattice spacing. We find that for $r > 0.2$~fm our results on the static energy agree with the ($2+1$)-flavor result, implying the decoupling of the charm quark for these distances. For smaller distances, on the other hand, we find that the effect of the dynamical charm quark is noticeable. The lattice results agree well with the two-loop perturbative expression of the static energy incorporating finite charm mass effects. This is the first time that the decoupling of the charm quark is observed and quantitatively analyzed on lattice data of the static energy.Comment: 50 pages, 37 figur

Requirements for resource networks compared to the state of the art. Deliverable D4.2

The primary aim of work package 4 is the development of methods supporting the concept of “Energy Efficiency 2.0”. This is a term coined for an approach which goes beyond the current effort to energy efficiency: introduction of technically efficient equipment, reduction of energy waste and mitigation of environmental pollution according to legislative requirements. “Energy Efficiency 2.0” is meant for companies which take a proactive approach in their management towards ecology and sustainability in general. A special concern in the matter is the integration of Renewable Energy Sources (RES) immediately in the production environment of manufacturing companies. For this purpose, a Resource Networks Methodology (RNM) is developed which is aimed to provide an approach which integrates all the different resources (as in requirements for a production operation) into factory planning and control methods. This deliverable details the theoretical background for the RNM and details the exact need for action as well as the requirements for development of the methodology. It discusses the motivation behind the push towards “Energy Efficiency 2.0” from a point of view of the European legislative, European standardisation bodies and the European markets. As RES and energy storages will be a major enabler or even requirement of the RNM, the available technologies and there characteristics are discussed. Furthermore, the state of the art on smart grids and micro grids is presented to give some background on other approaches which are being researched. The deliverable further summarises the state of the art in both science and practice on energy efficiency in production as one of the aspects to be integrated in the RNM. As flexibilities and volatilities are a prime concern of the RNM, a review of these in production systems has been made and is complemented with an overview of other projects considering the issue in relation with the integration of RES. Lastly, the need for action and the requirements for the further developments in Tasks 4.2 and 4.3 of the REEMAIN project are introduced. One example for such requirements is the placement of the RNM in the production system planning process (see Figure 1)