相关论文: Step Scaling with off-shell renormalisation

This paper is the fifth in a series devoted to the development of a rigorous renormalisation group method applicable to lattice field theories containing boson and/or fermion fields, and comprises the core of the method. In the…

On-shell amplitude methods allow to derive one-loop renormalization effects from just tree-level amplitudes, with no need of loop calculations. We derive a simple formula to obtain the anomalous dimensions of higher-dimensional operators…

Reverse Osmosis Membrane (ROM) filtration systems are widely applied in wastewater recovery, seawater desalination, landfill water treatment, etc. During filtration, the system performance is dramatically affected by membrane fouling which…

We study randomly stopped sums via their asymptotic scales. First, finiteness of moments is considered. To generalise this study, asymptotic scales applicable to the class of all heavy-tailed random variables are used. The stopping is…

Molecular dynamics simulations are widely used across chemistry, physics, and biology, providing quantitative insight into complex processes with atomic detail. However, their limited timescale of a few microseconds is a significant…

Recent exact predictions for the massive scaling limit of the two dimensional XY-model are based on the equivalence with the sine-Gordon theory and include detailed results on the finite size behavior. The so-called step-scaling function of…

The recent experimental progresses in handling microscopic systems have allowed to probe them at levels where fluctuations are prominent, calling for stochastic modeling in a large number of physical, chemical and biological phenomena. This…

A recently proposed renormalization scheme can be used to deal with nonrelativistic potential scattering exhibiting ultraviolet divergence in momentum space. A numerical application of this scheme is made in the case of potential scattering…

In neural network training, RMSProp and Adam remain widely favoured optimisation algorithms. One of the keys to their performance lies in selecting the correct step size, which can significantly influence their effectiveness. Additionally,…

We study the high-velocity regime mode-I fracture instability when small microbranches start to appear near the main crack, using large scale simulations. Some of the features of those microbranches have been reproduced qualitatively in…

We discuss a specific cut-off effect which appears in applying the non-perturbative RI/MOM scheme to compute the renormalization constants. To illustrate the problem a Dirac operator satisfying the Ginsparg-Wilson relation is used, but the…

We extend the theory of non-thermal fixed points to the case of anomalously slow universal scaling dynamics according to the sine-Gordon model. This entails the derivation of a kinetic equation for the momentum occupancy of the scalar field…

Tuning hyperparameters, such as the stepsize, presents a major challenge of training machine learning models. To address this challenge, numerous adaptive optimization algorithms have been developed that achieve near-optimal complexities,…

The estimation of normalizing constants is a fundamental step in probabilistic model comparison. Sequential Monte Carlo methods may be used for this task and have the advantage of being inherently parallelizable. However, the standard…

We discuss a stochastic closure for the equation of motion satisfied by multi-scale correlation functions in the framework of shell models of turbulence. We give a systematic procedure to calculate the anomalous scaling exponents of…

Shell model turbulence is a simplified mathematical framework that captures essential features of incompressible fluid turbulence such as the energy cascade, intermittency and anomalous scaling of the fluid observables. We perform a…

In these lectures, we discuss different types of renormalization problems in QCD and their non-perturbative solution in the framework of the lattice formulation. In particular the recursive finite size methods to compute the…

A general strategy to solve the non-perturbative renormalization problem in lattice QCD, using finite-size techniques and numerical simulations, is described. As an illustration we discuss the computation of the axial current normalization…

Models with classical scale symmetry, which feature radiative symmetry breaking, generically lead to a supercooled first-order phase transition in the early Universe resulting in a strong gravitational-wave signal, potentially observable by…

We present a new approach to determine the small-scale statistical behavior of hydrodynamic turbulence by means of lattice simulations. Using the functional integral representation of the random-force-driven Burgers equation we show that…