Long-Time Dynamics in Quantum Spin Lattices: Ergodicity and Hydrodynamic Projections at All Frequencies and Wavelengths
Long-Time Dynamics in Quantum Spin Lattices: Ergodicity and Hydrodynamic Projections at All Frequencies and Wavelengths
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DOI：
10.1007/s00023-023-01304-2
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发表时间：
2021-12
期刊：
影响因子：
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通讯作者：
Dimitrios Ampelogiannis;B. Doyon
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文献类型：
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作者：
Dimitrios Ampelogiannis;B. Doyon
得到关于扩展多体系统非平衡动力学的严格和一般性结果是一项困难的任务。在具有短程相互作用的量子晶格模型中，Lieb-Robinson束缚告诉我们，算子的空间范围随时间最多线性增长。但是在这个光锥中发生了什么呢？我们讨论严格的结果遍历性和相关函数，建立在非平衡物理学的根源的基本原则的欧拉流体动力学尺度的出现。本工作的一个关键思想是，一般结构的欧拉流体力学，弹道缩放下获得的，遵循独立的微观动力学的细节，特别是不需要混乱，它们是后果的“扩展性”。另一个重要的观察是，这些适用于任意频率和波长。也就是说，相关函数在时空弹道区域（可能具有微观频率和波长）上的长时间、持续振荡是由一般欧拉流体动力学理论预测的，该理论采用与平滑相关函数相同的形式。这涉及守恒量和流体动力学投影概念的自然扩展，并表明欧拉流体动力学范式涵盖了整个频率-波长平面。
Obtaining rigorous and general results about the non-equilibrium dynamics of extended many-body systems is a difficult task. In quantum lattice models with short-range interactions, the Lieb–Robinson bound tells us that the spatial extent of operators grows at most linearly in time. But what happens within this light-cone? We discuss rigorous results on ergodicity and the emergence of the Euler hydrodynamic scale in correlation functions, which establish fundamental principles at the root of non-equilibrium physics. One key idea of the present work is that general structures of Euler hydrodynamics, obtained under ballistic scaling, followindependently from the details of the microscopic dynamics, and in particular do not necessitate chaos; they are consequences of “extensivity”. Another crucial observation is that these apply atarbitrary frequencies and wavelengths. That is, long-time, persistent oscillations of correlation functions over ballistic regions of spacetime, which may be of microscopic frequencies and wavelengths, are predicted by a general Euler-hydrodynamic theory that takes the same form as that for smoothed-out correlation functions. This involves a natural extension of notions of conserved quantities and hydrodynamic projection and shows that the Euler hydrodynamic paradigm covers the full frequency-wavelength plane.