波动流体力学与虫洞
Fluctuating Hydrodynamics and Wormholes
摘要：
我们表明，最近重新制定的流体动力学方程的一个大类的模型组成的q-dits的图与短程相互作用是足够的理解混沌行为。任何这样的系统都是由相互作用耦合在一起的大型子系统组成的，这些子系统的相对强度随着子系统的大小而趋于零。在没有能量守恒定律的情况下，子系统的哈密顿算子形成了一个完整的交换算子集。流体动力学变量是子系统哈密尔顿算子的联合本征基中的密度矩阵的块对角矩阵元素$ρ(e(X))$，在能量箱上求平均。对于逆子系统尺寸的领先阶，$ρ(e(X); t)$满足经典的随机方程，对于某些系统，该随机方程采取泛函Fokker-Planck方程的形式。在这样的系统中，时间平均的频谱形状因子可以被写为具有多个不连通边界的空间上的二维欧几里德泛函积分。在这种表示法中因式分解的失败是由于应用流体动力近似所必需的时间平均。体欧几里德作用是纯拓扑的。我们尝试性地探索了系统的特殊性质，这些性质是将系统表示为度量上的函数积分所需的。
英文摘要：
We show that a recent reformulation of hydrodynamic equations for a large class of models consisting of q-dits on a graph with short range interactions is sufficient for understanding chaotic behavior. Any such system consists of large subsystems coupled together by interactions whose relative strength goes to zero with the subsystem size. In the absence of conservation laws other than energy, the Hamiltonians of the subsystems form a complete set of commuting operators. The hydrodynamic variables are the block diagonal matrix elements $ρ(e(X))$ of the density matrix in the joint eigenbasis of the subsystem Hamiltonians, averaged over energy bins. To leading order in the inverse subsystem size, $ρ(e(X); t)$ satisfies a classical stochastic equation, which for certain systems takes the form of a functional Fokker-Planck equation. In such systems the time averaged spectral form factors can be written as a two dimensional Euclidean functional integral, on a space with multiple disconnected boundaries. The failure of factorization in this representation is attributable to the time averaging necessary to apply the hydrodynamic approximation. The bulk Euclidean action is purely topological. We make tentative explorations of the special properties of the system that are required in order to have a representation as a functional integral over metrics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
