磁流体力学Kazantsev-Kraichnan模型中反常指数的双圈计算
Two-Loop Calculation of the Anomalous Exponents in the Kazantsev--Kraichnan Model of Magnetic Hydrodynamics
摘要：
本文在运动学近似的框架内，考虑了大尺度背景磁场存在下磁流体动力学湍流中的反常标度问题。本文将场论重整化群方法应用于Kazantsev-Kraichnan模型，该模型是由具有零均值和关联函数$\propto δ(t-t')/k^{d+ε}$的高斯速度场平流的被动矢量模型。惯性范围的反常标度的张量对指数的成立作为一个后果的存在，在相应的算子乘积展开的某些“危险”的复合算子，其负临界尺寸确定的反常指数。主要的技术成果是计算了$ε$展开（双环近似）的$ε^2$级的反常指数。
英文摘要：
The problem of anomalous scaling in magnetohydrodynamics turbulence is considered within the framework of the kinematic approximation, in the presence of a large-scale background magnetic field. Field theoretic renormalization group methods are applied to the Kazantsev-Kraichnan model of a passive vector advected by the Gaussian velocity field with zero mean and correlation function $\propto δ(t-t')/k^{d+ε}$. Inertial-range anomalous scaling for the tensor pair correlators is established as a consequence of the existence in the corresponding operator product expansions of certain "dangerous" composite operators, whose negative critical dimensions determine the anomalous exponents. The main technical result is the calculation of the anomalous exponents in the order $ε^2$ of the $ε$ expansion (two-loop approximation).
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