Stochastic quantization at finite chemical potential

Thirring model at finite density in 0+1 dimensions with stochastic quantization: Crosscheck with an exact solution

We consider a generalized Thirring model in 0+1 dimensions at finite density. In order to deal with the resulting sign problem we employ stochastic quantization, i.e., a complex Langevin evolution. We investigate the convergence properties of this approach and check in which parameter regions complex Langevin evolutions are applicable in this setting. To this end we derive numerous analytical results and compare directly with numerical results. In addition we employ indirect indicators to check for correctness. Finally we interpret and discuss our findings.

随机量子化与扩散模型

Stochastic quantization and diffusion models

本文以教学综述形式阐明扩散模型与随机量子化的 SDE 数学类比，并借助一维玩具模型和 Lefschetz thimble 分析解释复参数下符号问题的来源及通过核选择缓解的思路。

Thirring model at finite density in 2+1 dimensions with stochastic quantization

We consider a generalization of the Thirring model in 2+1 dimensions at finite density. We employ stochastic quantization and check for the applicability in the finite density case to circumvent the sign problem. To this end we derive analytical results in the heavy dense limit and compare with numerical ones obtained from a complex Langevin evolution. Furthermore we make use of indirect indicators to check for incorrect convergence of the underlying complex Langevin evolution. The method allows the numerical evaluation of observables at arbitrary values of the chemical potential. We evaluate …

Cooling Stochastic Quantization with colored noise

Smoothing of field configurations is highly important for precision calculations of physical quantities on the lattice. We present a cooling method based on Stochastic Quantization with a built-in UV momentum cutoff. The latter is implemented via a UV-regularized, hence colored, noise term. Our method is tested in a two-dimensional scalar field theory. We show, that UV modes can be removed systematically without altering the physics content of the theory. The approach has an interpretation in terms of the non-perturbative (Wilsonian) renormalization group that facilitates the physics interpret…

随机量化与离散虚时间

Stochastic quantization with discrete fictitious time

本文提出一种基于离散虚时间的随机量化方法，通过权重修改噪声平均，实现无需连续极限的量子场理论相关函数等价，并在零维模型中进行了验证。

Two infrared Yang-Mills solutions in stochastic quantization and in an effective action formalism

Three decades of work on the quantum field equations of pure Yang-Mills theory have distilled two families of solutions in Landau gauge. Both coincide for high (Euclidean) momentum with known perturbation theory, and both predict an infrared suppressed transverse gluon propagator, but whereas the solution known as "scaling" features an infrared power law for the gluon and ghost propagators, the "massive" solution rather describes the gluon as a vector boson that features a finite Debye screening mass. In this work we examine the gauge dependence of these solutions by adopting stochastic quanti…

Stochastic quantization of a self-interacting nonminimal scalar field in semiclassical gravity

We employ stochastic quantization for a self-interacting nonminimal massive scalar field in curved spacetime. The covariant background field method and local momentum space representation are used to obtain the Euclidean correlation function and evaluate multi-loop quantum corrections through simultaneous expansions in the curvature tensor and its covariant derivatives and in the noise fields. The stochastic correlation function reproduces the well-known result by Bunch and Parker and is used to construct the effective potential in curved spacetime in an arbitrary dimension $D$ up to the first…

作为最优控制的随机量子化

Stochastic Quantization as Optimal Control

研究将随机量子化表述为有限时间随机最优控制问题，利用可处理参考过程及参考校正终端成本，通过神经网络学习残余控制实现最优随机量子化，在多峰势和二维晶格标量\(\phi^4\)理论中取得成果，将量子化表述为控制。

Momentum Lattice Simulation on a Small Lattice Using Stochastic Quantization

We have studied the scalar $ϕ^4$-model in the symmetric phase and the non--compact $U(1)$ gauge theory on a momentum lattice using the Langevin equation for generating configurations. In the $ϕ^4$-model we have analyzed the renormalized mass and in the $U(1)$-model we have analyzed the Wilson loop operator. We used a second order algorithm for solving the Langevin equation, and we looked for the convergence rate of the method. We studied the stochastic time needed to generate equilibrium configurations and compared first and second order schemes for both models.

格点场论中作为随机量子化的扩散模型

Diffusion Models as Stochastic Quantization in Lattice Field Theory

本文建立扩散模型与随机量子化的直接联系，并在二维$\phi^4$理论中验证其可作为全局采样器，显著降低临界区Markov链自相关时间。