论文标题
从量子和经典微观动力学衍生的欧拉方程
Derivation of Euler equations from quantum and classical microscopic dynamics
论文作者
论文摘要
我们从哈密顿的微观动力学中得出欧拉方程。微观系统是一维无序的谐波链，动力学是量子或经典的。该链是具有对称性保护模式的Anderson绝缘子：热波动被冷冻，而低模式确保伸长，动量和机械能的传输，这些延伸，动量和机械能，根据Euler方程在双曲缩放尺度上的发展。在本文中，我们大大加强了以前的结果，在该结果中，我们从本地吉布斯状态开始建立了平均值的限制：我们现在控制着平均值左右波动的第二刻，产生了概率的限制，并扩大了可允许的初始状态的类别。
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.
