论文标题
无序量子谐波链的流体动力极限
Hydrodynamic limit for a disordered quantum harmonic chain
论文作者
论文摘要
在本说明中，我们研究具有随机质量的一维量子谐波振荡器的双曲线时空缩放中的流体动力极限。据我们所知，这是第一个示例之一，在该例子中可以严格证明量子系统的流体动力极限。实际上，我们证明，在时间和空间的双曲线重新缩放后，在适当的吉布斯状态下平均的伸长，动量和能量的分布会收敛到Euler方程的溶液。该链中有两个主要现象，使我们能够推断出这一结果。首先是安德森定位，它解开了机械和热能，提供了能量方程的关闭，并表明温度曲线将被冷冻。第二种现象类似于某种相关现象的衰减，这使我们避免了由于系统的量子性质而导致的吉布斯状态不是产品状态而引起的困难。
In this note, we study the hydrodynamic limit, in the hyperbolic space-time scaling, for a one-dimensional unpinned chain of quantum harmonic oscillators with random masses. To the best of our knowledge, this is among the first examples, where one can prove the hydrodynamic limit for a quantum system rigorously. In fact, we prove that after hyperbolic rescaling of time and space the distribution of the elongation, momentum, and energy averaged under the proper Gibbs state, converges to the solution of the Euler equation. There are two main phenomena in this chain which enable us to deduce this result. First is the Anderson localization which decouples the mechanical and thermal energy, providing the closure of the equation for energy and indicating that the temperature profile will be frozen. The second phenomena is similar to some sort of decay of correlation phenomena which let us circumvent the difficulties arising from the fact that our Gibbs state is not a product state due to the quantum nature of the system.
