论文标题
自磨的玻色气和非本地非线性光学的波湍流
Wave turbulence in self-gravitating Bose gases and nonlocal nonlinear optics
论文作者
论文摘要
我们在由schrödinger-Helmholtz方程描述的两个和三个维度中描述的系统中发展了弱波湍流的理论。该模型包含限制熟悉的立方体非线性Schrödinger方程和Schrödinger-Newton方程。后者在三个维度上是模糊暗物质的非层次主义模型，它具有非本地引力自势，在两个维度中，它们描述了在偏移近似中的非局部非线性光学。我们表明，在弱非线性限制中，schrödinger-helmholtz方程具有同时的粒子反向级联和向前的能量级联。我们将反级联反向级联解释为非平衡冷凝过程，这是在大尺度上结构形成的先驱（例如，银河系暗物质光环或光学孤子的形成）。我们表明，对于在两个和三个维度上的Schrödinger-Newton方程，在二维非线性Schrödinger方程中，粒子和能量通量是由与热力学分布的小偏差相比，而不是kolmogorov-Zakharov级联，这些级子在波浪湍流中熟悉。我们开发一个差异近似模型来表征这种“温暖级联”状态。
We develop the theory of weak wave turbulence in systems described by the Schrödinger-Helmholtz equations in two and three dimensions. This model contains as limits both the familiar cubic nonlinear Schrödinger equation, and the Schrödinger-Newton equations. The latter, in three dimensions, are a nonrelativistic model of fuzzy dark matter which has a nonlocal gravitational self-potential, and in two dimensions they describe nonlocal nonlinear optics in the paraxial approximation. We show that in the weakly nonlinear limit the Schrödinger-Helmholtz equations have a simultaneous inverse cascade of particles and a forward cascade of energy. We interpret the inverse cascade as a nonequilibrium condensation process, which is a precursor to structure formation at large scales (for example the formation of galactic dark matter haloes or optical solitons). We show that for the Schrödinger-Newton equations in two and three dimensions, and in the two-dimensional nonlinear Schrödinger equation, the particle and energy fluxes are carried by small deviations from thermodynamic distributions, rather than the Kolmogorov-Zakharov cascades that are familiar in wave turbulence. We develop a differential approximation model to characterise such "warm cascade" states.
