论文标题
Feynman强迫波湍流规则
Feynman rules for forced wave turbulence
论文作者
论文摘要
长期以来，众所周知，弱的非线性场理论可以具有不是热状态的延迟固定状态，而是具有远程平衡能量级联的波湍流状态。我们超越了波湍流状态的存在，研究了有关波湍流状态的波动。具体而言，我们采用了一种具有任意四分之一相互作用的经典字段理论，并增加了耗散和高斯随机强迫。利用随机经典字段理论和量子场理论之间的路径积分关系，我们在Feynman图方面给出了一个处方，以计算该系统中的相关功能。我们将字段的两点和四点函数明确计算到耦合中的临时顺序。通过适当的强迫和耗散选择，这些对应于波湍流状态下的相关函数。特别是，我们将动力学方程式得出近来的顺序。
It has long been known that weakly nonlinear field theories can have a late-time stationary state that is not the thermal state, but a wave turbulent state with a far-from-equilibrium cascade of energy. We go beyond the existence of the wave turbulent state, studying fluctuations about the wave turbulent state. Specifically, we take a classical field theory with an arbitrary quartic interaction and add dissipation and Gaussian-random forcing. Employing the path integral relation between stochastic classical field theories and quantum field theories, we give a prescription, in terms of Feynman diagrams, for computing correlation functions in this system. We explicitly compute the two-point and four-point functions of the field to next-to-leading order in the coupling. Through an appropriate choice of forcing and dissipation, these correspond to correlation functions in the wave turbulent state. In particular, we derive the kinetic equation to next-to-leading order.
