Related papers: Implications of gradient flow on the static force
We revisit force evaluation methodologies on rigid solid particles suspended in a viscous fluid and simulated via lattice Boltzmann method (LBM). We point out the non-commutativity of streaming and collision operators in the force…
The static energy is an excellent observable for extracting the strong coupling $\alpha_s$ on the lattice. For short distances, the static energy can be calculated both on the lattice using Wilson line correlators, and with perturbation…
Recently, the Yang-Mills gradient flow is found to be a useful concept not only in lattice simulations but also in continuous field theories. Since its smearing property is similar to the Wilsoninan "block spin transformation", there might…
We present the expansion of stout smearing and the Wilson flow in lattice perturbation theory to order $g_0^3$, which is suitable for one-loop calculations. As the Wilson flow is generated by infinitesimal stout smearing steps, the results…
The gradient-flow formulation of the energy-momentum tensor of QCD is extended to NNLO perturbation theory. This means that the Wilson coefficients which multiply the flowed operators in the corresponding expression for the regular…
We introduce and implement a method to compute stationary states of nonlinear Schr\''odinger equations on metric graphs. Stationary states are obtained as local minimizers of the nonlinear Schr\''odinger energy at fixed mass. Our method is…
We perform the scale setting procedure of a mixed action setup consisting of valence Wilson twisted mass fermions at maximal twist on CLS ensembles with $N_f=2+1$ flavours of $O(a)$-improved Wilson sea quarks. We determine the gradient flow…
The gradient flow in QCD is treated perturbatively through next-to-next-to-leading order in the strong coupling constant. The evaluation of the relevant momentum and flow-time integrals is described, including various means of validation.…
We present results from an ongoing project concerned with the computation of $\mathcal{O}(1/m_Q)$ and $\mathcal{O}(1/m_Q^2)$ relativistic corrections to the static potential. These corrections are extracted from Wilson loops with two…
The Yang-Mills gradient flow and the observable E(t), defined by the square of the field strength tensor at t>0, are calculated at finite lattice spacing and tree-level in the gauge coupling. Improvement of the flow, the gauge action and…
Theoretical and numerical studies of the Wilson flow in lattice QCD suggest that the gauge field obtained at flow time t>0 is a smooth renormalized field. The expectation values of local gauge-invariant expressions in this field are thus…
When designing lattice actions, gauge field smearing is often used in the definition of the lattice Dirac operator. Too much smearing can result in uncontrolled continuum extrapolations as the short distance behaviour of the theory is…
We study the perturbative behavior of the Yang-Mills gradient flow in the Schr\"odinger Functional, both in the continuum and on the lattice. The energy density of the flow field is used to define a running coupling at a scale given by the…
We discuss the non-perturbative computation and interpretation of a colour adjoint static potential based on Wilson loops with generator insertions. Numerical lattice results for SU(2) gauge theory are presented and compared to…
The gradient (Wilson) flow has been introduced recently in order to provide a solid theoretical framework for the smoothing of ultraviolet noise in lattice gauge configurations. It is interesting to ask how it compares with other, more…
We review the gradient flow for gauge and fermion fields and its applications to lattice gauge theory computations. Using specific examples, we discuss the interplay between perturbative and non-perturbative calculations in the context of…
The static local-field factor (LFF) of the interacting 2-D fluid is calculated nonperturbatively using a mapping of the quantum fluid to a classical Coulomb fluid [Phys. Rev. Let., {\bf 87}, 206 (2002)]. The LFF for the paramagnetic fluid…
We present a recursive formula for the computation of the static effective Hamiltonian of a system under a fast-oscillating drive. Our analytical result is well-suited to symbolic calculations performed by a computer and can be implemented…
The gradient flow method is a renormalization scheme in which the gauge field is flowed by the diffusion equation. The gradient flow scheme has benefits that the observables composed of flowed gauge fields do not require further…
I analyze cutoff effects of the gradient flow for Wilson-type fermions. I show that with a proper choice of the higher dimensional fields in the Symanzik effective theory, O($a$) improvement of the action is achieved changing the initial…