论文标题
波湍流和动力学方程超出领先顺序
Wave turbulence and the kinetic equation beyond leading order
论文作者
论文摘要
我们得出了一个方案，该方案在非线性中依赖于liouville方程，我们将其应用于弱非线性经典的现场理论。我们的解决方案是prigogine示意法的变体，它基于Lippmann-Schwinger方程描述的无限体积的Liouville方程与量子力学中的散射之间的类比。我们工作的动机是波动湍流：据信一类广泛的非线性古典田地理论具有固定的湍流状态 - 即使是在弱耦合下，也很远。我们的方法提供了一种有效的方法来得出弱波湍流状态的性能。这些研究中的一个中心对象是减少liouville方程式的动力学方程，该方程控制模式的职业数量。迄今为止的波湍流的所有特性均基于在弱非线性中的领先顺序上发现的动力学方程。我们明确获取动力学方程式到近代领导顺序。
We derive a scheme by which to solve the Liouville equation perturbatively in the nonlinearity, which we apply to weakly nonlinear classical field theories. Our solution is a variant of the Prigogine diagrammatic method, and is based on an analogy between the Liouville equation in infinite volume and scattering in quantum mechanics, described by the Lippmann-Schwinger equation. The motivation for our work is wave turbulence: a broad class of nonlinear classical field theories are believed to have a stationary turbulent state -- a far-from-equilibrium state, even at weak coupling. Our method provides an efficient way to derive properties of the weak wave turbulent state. A central object in these studies, which is a reduction of the Liouville equation, is the kinetic equation, which governs the occupation numbers of the modes. All properties of wave turbulence to date are based on the kinetic equation found at leading order in the weak nonlinearity. We explicitly obtain the kinetic equation to next-to-leading order.
