宇宙发电机模拟与三维Ricci流中磁场的衰减
Cosmic dynamo analogue and decay of magnetic fields in 3D Ricci flows
摘要：
Barrow和Tsagas（BT）[Phys Rev D \textbf{77}，（2008）]研究的磁曲率效应作为开放弗里德曼宇宙（$Λ<0$）中磁场衰减的机制，在实验室中应用于三维弯曲基底中的发电机几何Ricci流。通过简单的推导，得到了一个协变的三维磁自感方程，并指出了这些曲率效应的存在，即de Sitter宇宙学常数（$Λ\ge{0}$）导致了快速运动发电机作用的增强，从而增加了等离子体流的拉伸。从磁增长率来看，强剪切情况下，反德西特情况（$Λ<0$）BT磁衰减场是可能的，而对于弱剪切，快速发电机是可能的。Ricci流中的自诱导方程与BT在$(3+1)$ -时空连续体中导出的方程相似。Lyapunov-de Sitter度量由Ricci流特征值问题得到。在de Sitter模拟中，从相应的宇宙学常数$Λ$到$γ\approx{-Λ}\approx{-10^{-35}s^{-2}}$的衰减率表明，即使在发电机的情况下，磁场的增长也比de Sitter暴胀慢，这有力地支持了BT结果.
英文摘要：
Magnetic curvature effects, investigated by Barrow and Tsagas (BT) [Phys Rev D \textbf{77},(2008)],as a mechanism for magnetic field decay in open Friedmann universes ($Λ<0$), are applied to dynamo geometric Ricci flows in 3D curved substrate in laboratory. By simple derivation, a covariant three-dimensional magnetic self-induced equation, presence of these curvature effects, indicates that de Sitter cosmological constant ($Λ\ge{0}$), leads to enhancement in the fast kinematic dynamo action which adds to stretching of plasma flows. From the magnetic growth rate, the strong shear case, anti-de Sitter case ($Λ<0$) BT magnetic decaying fields are possible while for weak shear, fast dynamos are possible. The self-induced equation in Ricci flows is similar to the equation derived by BT in $(3+1)$-spacetime continuum. Lyapunov-de Sitter metric is obtained from Ricci flow eigenvalue problem. In de Sitter analogue there is a decay rate of $γ\approx{-Λ}\approx{-10^{-35}s^{-2}}$ from corresponding cosmological constant $Λ$, showing that, even in the dynamo case, magnetic field growth is slower than de Sitter inflation, which strongly supports to BT result.
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