Hydrodynamic Projections and the Emergence of Linearised Euler Equations in One-Dimensional Isolated Systems
Hydrodynamic Projections and the Emergence of Linearised Euler Equations in One-Dimensional Isolated Systems
复制标题
一维孤立系统中的流体动力学投影和线性化欧拉方程的出现
DOI：
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发表时间：
2020
影响因子：
2.4
通讯作者：
B. Doyon
中科院分区：
文献类型：
--
作者：
B. Doyon
One of the most profound questions of mathematical physics is that of establishing from first principles the hydrodynamic equations in large, isolated, strongly interacting many-body systems. This involves understanding relaxation at long times under reversible dynamics, determining the space of emergent collective degrees of freedom (the ballistic waves), showing that projection occurs onto them, and establishing their dynamics (the hydrodynamic equations). We make progress in these directions, focussing for simplicity on one-dimensional systems. Under a model-independent definition of the complete space of extensive conserved charges, we show that hydrodynamic projection occurs in Euler-scale two-point correlation functions. A fundamental ingredient is a property of relaxation: we establish ergodicity of correlation functions along almost every direction in space and time. We further show that to every extensive conserved charge with a local density is associated a local current and a continuity equation; and that Euler-scale two-point correlation functions of local conserved densities satisfy a hydrodynamic equation. The results are established rigorously within a general framework based on Hilbert spaces of observables. These spaces occur naturally in the C∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^*$$\end{document} algebra description of statistical mechanics by the Gelfand–Naimark–Segal construction. Using Araki’s exponential clustering and the Lieb–Robinson bound, we show that the results hold, for instance, in every nonzero-temperature Gibbs state of short-range quantum spin chains. Many techniques we introduce are generalisable to higher dimensions. This provides a precise and universal theory for the emergence of ballistic waves at the Euler scale and how they propagate within homogeneous, stationary states.
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影响因子：
56.9
作者：
Langen, Tim;Erne, Sebastian;Schmiedmayer, Joerg
通讯作者：
Schmiedmayer, Joerg
影响因子：
56.9
作者：
N. Malvania;Yicheng Zhang;Yuan Le;J. Dubail;M. Rigol;D. Weiss
通讯作者：
N. Malvania;Yicheng Zhang;Yuan Le;J. Dubail;M. Rigol;D. Weiss
流体动力学投影的扩散和超扩散
影响因子：
1.6
作者：
Doyon B
通讯作者：
Doyon B
影响因子：
16.6
作者：
Buca, Berislav;Tindall, Joseph;Jaksch, Dieter
通讯作者：
Jaksch, Dieter
量子格模型中几乎无处不在的遍历性
影响因子：
2.4
作者：
Ampelogiannis D
通讯作者：
Ampelogiannis D