Quasi-Monte Carlo methods for lattice systems: A first look

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)

Abstract
We investigate the applicability of quasi-Monte Carlo methods to Euclidean lattice systems for quantum mechanics in order to improve the asymptotic error behavior of observables for such theories. In most cases the error of an observable calculated by averaging over random observations generated from an ordinary Markov chain Monte Carlo simulation behaves like N − 1 / 2 , where N is the number of observations. By means of quasi-Monte Carlo methods it is possible to improve this behavior for c...

Title of program: qar-0.1
Catalogue Id: AERJ_v1_0

Nature of problem
Certain physical models formulated as a quantum field theory through the Feynman path integral, such as quantum chromodynamics, require a non-perturbative treatment of the path integral. The only known approach that achieves this is the lattice regularisation. In this formulation the path integral is discretised to a finite, but very high dimensional integral. So far only Monte Carlo, and especially Markov chain-Monte Carlo methods like the Metropolis or the hybrid Monte Carlo algorithm have bee ...

Versions of this program held in the CPC repository in Mendeley Data
AERJ_v1_0; qar-0.1; 10.1016/j.cpc.2013.10.011

本程序源自贝尔法斯特女王大学（1969-2018年）所藏的CPC程序库。

摘要：本研究旨在探讨准蒙特卡洛方法在欧几里得晶格系统中应用于量子力学理论，以期改善此类理论中可观察量的渐近误差行为。在大多数情况下，通过从普通马尔可夫链蒙特卡洛模拟中生成的随机观测值进行平均计算的可观察量误差行为呈现为N的-1/2次方，其中N代表观测值的数量。借助准蒙特卡洛方法，可以改善这种行为，对于c...

程序标题：qar-0.1

目录编号：AERJ_v1_0

问题性质：某些物理模型，如通过费曼路径积分公式化的量子场论（例如量子色动力学），需要非微扰处理路径积分。目前实现此目的的唯一已知方法为晶格正则化。在该公式中，路径积分被离散化为有限但维度极高的积分。迄今为止，仅蒙特卡洛方法，尤其是如Metropolis或混合蒙特卡洛算法之类的马尔可夫链蒙特卡洛方法被用于此...

CPC存储库中Mendeley数据中保存的此程序版本：AERJ_v1_0; qar-0.1; 10.1016/j.cpc.2013.10.011