广义流体力学的几何观点
A geometric viewpoint on generalized hydrodynamics
摘要：
广义流体力学（GHD）是研究多体可积系统动力学的大尺度理论。它由一组无限的守恒定律组成，这些守恒定律适用于准粒子，它们以取决于局部状态的有效（“修饰”）速度运动。我们表明，这些方程可以重铸成一个几何动力学问题。它们是具有与状态无关的准粒子速度的守恒方程，在一个配备了一系列度量的空间中，由准粒子的类型和速度参数化，取决于局部状态。在经典硬棒或孤子气体图像中，这些度规测量准粒子所感知的空间自由长度，在量子图像中，它们用它们可用的态密度来衡量空间。使用这种几何结构，我们找到了一般的解决方案GHD的初值问题，在一组积分方程的时间出现明确。这些积分方程可通过迭代求解，并为GHD提供了一种非常有效的求解算法。
英文摘要：
Generalized hydrodynamics (GHD) is a large-scale theory for the dynamics of many-body integrable systems. It consists of an infinite set of conservation laws for quasi-particles traveling with effective ("dressed") velocities that depend on the local state. We show that these equations can be recast into a geometric dynamical problem. They are conservation equations with state-independent quasi-particle velocities, in a space equipped with a family of metrics, parametrized by the quasi-particles' type and speed, that depend on the local state. In the classical hard rod or soliton gas picture, these metrics measure the free length of space as perceived by quasi-particles, in the quantum picture, they weigh space with the density of states available to them. Using this geometric construction, we find a general solution to the initial value problem of GHD, in terms of a set of integral equations where time appears explicitly. These integral equations are solvable by iteration and provide an extremely efficient solution algorithm for GHD.
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