论文标题
迭代平均场方法，用于暗物质光环的球形崩溃
Iterative mean-field approach to the spherical collapse of dark matter halos
论文作者
论文摘要
暗物质过度的引力崩溃导致形成暗物质的嵌入星系和星系簇。暗物质光环的一个有趣的特征是，它们的密度曲线非常遵循通用形式，而与初始条件或相应的生长历史无关。这代表了具有新兴普遍性的一类动力系统。我们提出了一种“迭代平均场方法”来计算重力塌陷动力学的解决方案。这种方法迭代地搜索交互场的演变$ ϕ（t）$ - 在这种情况下，在这种情况下，封闭的质量配置文件$ m（r，t）$ - 与动力学一致，因此$ ϕ（t）$是迭代映射的修复点，$ \ mathcal {h}（h}（ϕ）= ϕ $。形式主义将N体相互作用用与粗粒粒子相互作用场的一体相互作用取代，从而在统计物理学中分享了平均场理论的精神。这种“迭代平均场方法”结合了数值模拟的多功能性和分析解决方案的全面性，并且在搜索和理解中间渐近状态的广泛动力学系统中特别有力，在这些系统中，无法通过传统的自相似分析获得该解决方案。
Gravitational collapse of dark matter overdensities leads to the formation of dark matter halos which embed galaxies and galaxy clusters. An intriguing feature of dark matter halos is that their density profiles closely follow a universal form irrespective of the initial condition or the corresponding growth history. This represents a class of dynamical systems with emergent universalities. We propose an "iterative mean-field approach" to compute the solutions of the gravitational collapse dynamics. This approach iteratively searches for the evolution of the interaction field $ϕ(t)$ -- in this case the enclosed mass profile $M(r,t)$ -- that is consistent with the dynamics, thus that $ϕ(t)$ is the fix-point of the iterative mapping, $\mathcal{H}(ϕ) = ϕ$. The formalism replaces the N-body interactions with one-body interactions with the coarse-grained interaction field, and thus shares the spirit of the mean-field theory in statistical physics. This "iterative mean-field approach" combines the versatility of numerical simulations and the comprehensiveness of analytical solutions, and is particularly powerful in searching for and understanding intermediate asymptotic states in a wide range of dynamical systems where the solutions can not be obtained through the traditional self-similar analysis.
