Generalized Hydrodynamics is a recent theory that describes large scale transport properties of one dimensional integrable models. It is built on the (typically infinitely many) local conservation laws present in these systems, and leads to a generalized Euler type hydrodynamic equation. Despite the successes of the theory, one of its cornerstones, namely a conjectured expression for the currents of the conserved charges in local equilibrium has not yet been proven for interacting lattice models. Here we fill this gap, and compute an exact result for the mean values of current operators in Bethe Ansatz solvable systems, valid in arbitrary finite volume. Our exact formula has a simple semi-classical interpretation: the currents can be computed by summing over the charge eigenvalues carried by the individual bare particles, multiplied with an effective velocity describing their propagation in the presence of the other particles. Remarkably, the semi-classical formula remains exact in the interacting quantum theory, for any finite number of particles and also in the thermodynamic limit. Our proof is built on a form factor expansion and it is applicable to a large class of quantum integrable models.

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Bethe Ansatz和广义流体力学中的当前算符：精确的量子/经典对应

广义流体动力学是描述一维可积模型的大规模输运性质的最新理论。它建立在这些系统中存在的（通常是无限多个）局部守恒定律的基础上，并得出了广义的Euler型流体动力学方程。尽管该理论取得了成功，但它的基石之一，即局部平衡中守恒电荷流的一种推测表达式，尚未得到相互作用晶格模型的证明。在这里，我们填补了这一空白，并计算了Bethe Ansatz可解系统中当前算子平均值的精确结果，该结果在任意有限体积内均有效。我们的精确公式具有简单的半经典解释：可以通过将各个裸粒子所携带的电荷特征值相加来计算电流，用有效速度乘以描述它们在其他粒子存在下的传播。值得注意的是，对于任何有限数量的粒子，在热力学极限中，半经典公式在相互作用的量子理论中都保持精确。我们的证明建立在形状因子扩展的基础上，并且适用于一大类量子可积模型。