We derive Euler equations from a Hamiltonian microscopic dynamics. The microscopic system is a one-dimensional disordered harmonic chain, and the dynamics is either quantum or classical. This chain is an Anderson insulator with a symmetry protected mode: Thermal fluctuations are frozen while the low modes ensure the transport of elongation, momentum and mechanical energy, that evolve according to Euler equations in an hyperbolic scaling limit. In this paper, we strengthen considerably our previous results, where we established a limit in mean starting from a local Gibbs state: We now control the second moment of the fluctuations around the average, yielding a limit in probability, and we enlarge the class of admissible initial states.

中文翻译：

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从量子和经典微观动力学推导欧拉方程

我们从哈密顿微观动力学推导出欧拉方程。微观系统是一维无序的谐波链，动力学要么是量子的，要么是经典的。该链是具有对称保护模式的安德森绝缘体：热波动被冻结，而低模式确保伸长、动量和机械能的传输，它们根据欧拉方程在双曲线缩放限制中演变。在本文中，我们大大加强了我们之前的结果，我们从局部吉布斯状态开始建立了平均值的极限：我们现在控制平均值附近波动的第二时刻，产生概率极限，并且我们扩大了类别可接受的初始状态。