相关论文: Lattice worldline representation of correlators in…

We consider a discrete random walk on a diagonal lattice in two and three dimensions and obtain explicit solutions of absorption probabilities and probabilities of return in several domains. In three dimensions we consider both the cube and…

In this article we introduce theory and algorithms for learning discrete representations that take on a lattice that is embedded in an Euclidean space. Lattice representations possess an interesting combination of properties: a) they can be…

We present a method of computing any one-loop integral in lattice perturbation theory by systematically expanding around its continuum limit. At any order in the expansion in the lattice spacing, the result can be written as a sum of…

We exhibit simple lattice systems, motivated by recently proposed cold atom experiments, whose continuum limits interpolate between real and $p$-adic smoothness as a spectral exponent is varied. A real spatial dimension emerges in the…

Bi-adjoint scalars are helpful in studying properties of color/kinematics duality and the double copy, which relates scattering amplitudes of gauge and gravity theories. Here we study bi-adjoint scalars from a worldline perspective. We show…

We propose to calculate bosonic and fermionic determinants with some general field background, and the corresponding 1-loop effective actions by evaluating random walk worldline loops generated statistically on the lattice. This is…

We investigate active lattice walks: biased continuous time random walks which perform orientational diffusion between lattice directions in one and two spatial dimensions. We study the occupation probability of an arbitrary site on the…

A gauge invariant Hamiltonian representation for SU(2) in terms of a spin network basis is introduced. The vectors of the spin network basis are independent and the electric part of the Hamiltonian is diagonal in this representation. The…

Using techniques from hopping expansion we identically map the lattice Schwinger model with Wilson fermions to a model of oriented loops on the lattice. This is done by first computing the explicit form of the fermion determinant in the…

Using a connection between the $q$-oscillator algebra and the coefficients of the high temperature expansion of the frustrated Gaussian spin model, we derive an exact formula for the number of closed random walks of given length and area,…

We present a comprehensive discussion on lattice techniques for the simulation of scalar and gauge field dynamics in an expanding universe. After reviewing the continuum formulation of scalar and gauge field interactions in Minkowski and…

We examine simulations of the formation of domain walls, cosmic strings, and monopoles on a cubic lattice, in which the topological defects are assumed to lie at the zeros of a piecewise constant 1, 2, or 3 component Gaussian random field,…

The eigenvalue spectrum $\rho(\lambda)$ of the Dirac operator is numerically calculated in lattice QCD with 2+1 flavors of dynamical domain-wall fermions. In the high-energy regime, the discretization effects become significant. We subtract…

We construct numerical basis function sets on a lattice, whose spatial extension is scalable from single lattice sites to the continuum limit. They allow us to compute small and large bound states with comparable, moderate effort. Adopting…

We study an homogeneous irreducible markovian random walk in a square lattice of arbitrary dimension, with an antisymmetric perturbation acting only in one point. We compute exactly spatial correction to the diffusive behaviour in the…

We study the lattice random walk dynamics in a heterogeneous space of two media separated by an interface and having different diffusivity and bias. Depending on the position of the interface, there exist two exclusive ways to model the…

A variety of transport processes in natural and man-made systems are intrinsically random. To model their stochasticity, lattice random walks have been employed for a long time, mainly by considering Cartesian lattices. However, in many…

Holographic Conformal Field Theories (CFTs) are usually studied in a limit where the gravity description is weakly coupled. By contrast, lattice quantum field theory can be used as a tool for doing computations in a wider class of…

We study the path behavior of the anisotropic random walk on the two-dimensional lattice Z^2. Simultaneous strong approximations of its components are given.

Because of the mass gap, lattice QCD simulations exhibit stochastic locality: distant regions of the lattice fluctuate independently. There is a long history of exploiting this to increase statistics by obtaining multiple…