非马尔可夫性的随机正则化数值模拟
Numerical simulation of the stochastic formalism including non-Markovianity
AI总结：
本文基于de Sitter背景，研究非马尔可夫性在宇宙学随机动力学中的影响，通过求解IR和UV模式的朗之万方程，发现有效质量处理一致时，MSSM中的平坦方向保持平坦，并探讨了非马尔可夫贡献在强耦合 regime 中的显著影响。
摘要：
我们通过求解红外（IR）模式的朗之万方程，研究宇宙学中的随机动力学，其中随机噪声由紫外（UV）模式在粗粒化尺度上生成。通过构造，随机正则化依赖于尺度分离，这要求在所有模式上，在每个时间步中求解UV模式的方程，从而通常导致非马尔可夫系统。在本文中，我们基于de Sitter背景，通过同时求解IR模式和UV模式的朗之万方程，分析了几种代表性模型。我们证明，一旦通过我们的模拟一致处理有效质量的影响，最小超对称模型（MSSM）中的平坦方向不会饱和，而是作为精确的平坦方向演变。此外，我们研究了简单两种模型中的记忆效应；V=λϕ^4和V=μϕχ+λϕ^4，非马尔可夫贡献可以在静态配置中与马尔可夫近似产生定量差异，特别是在强耦合 regime 中。
英文摘要：
We numerically investigate stochastic dynamics in cosmology by solving Langevin equations for Infrared (IR) modes with stochastic noises generated by Ultraviolet (UV) modes at the coarse-graining scale. By construction, the stochastic formalism relies on the separation of scales, which requires solving the equations for UV modes on top of the evolving IR modes for all modes at every time step, leading to a non-Markovian system in general. In this paper, working on a de Sitter background, we analyze several representative models by simultaneously solving the Langevin equations for IR modes and the equations for UV modes at each time step. We demonstrate that once the effects of effective masses are treated consistently by our simulation, the flat direction in the minimal supersymmtric model (MSSM) does not saturate but instead evolves as an exactly flat direction. Furthermore, we investigate memory effects in simple two models; $V=λϕ^4$ and $V=μϕχ+ λϕ^4$, and non-Markovian contributions can lead to quantitative differences, even in stationary configurations, when compared with Markovian approximations, particularly in the strong-coupling regime.
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