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Fluctuations and correlations at large scales from emergent hydrodynamics: integrable systems and beyond

新兴流体动力学中的大规模波动和相关性：可积系统及其他

基本信息

批准号：
EP/W010194/1
负责人：
Benjamin Doyon
金额：
$ 64.34万
依托单位：
King's College London
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2022
资助国家：
英国
起止时间：
2022 至无数据
项目状态：
未结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FW010194%2F1
关键词：
Fluctuations correlations large scales emergent

项目摘要

Gases and fluids are composed of a very large number of particles that interact with each other. Because of the interaction, chaos makes it difficult, in fact practically impossible, to predict the particles' trajectories. This is true even if there were just three particles, a fortiori with a large number of them. But, with a large number of particles, there's another simplification that occurs: if we forget about the individual trajectories and instead look at what happens when seen "from far", the system becomes again simple to describe. Essentially, trajectories average out, and what emerges, at large observation scales, is simpler, smoother, and described by a reduced number of effective degrees of freedom. No need to know all trajectories of water molecules in order to determine how waves propagate: the wave equations are much simpler. This is hydrodynamics, and waves are the emergent degrees of freedom.Surprisingly, hydrodynamics is a set of ideas that goes much beyond water and other simple fluids: it describes eletrons in metal, quasi-one-dimensional quantum ultracold Rubidium atoms in modern experiments, spins in magnetic materials, and much more. In fact, even more surprisingly, it was found recently that chaos is not necessary for hydrodynamics to occur. For systems that are "integrable" - a mathematical property that implies that with few particles, the trajectoris can be fully calculated and there is no chaos - still the ideas of hydrodynamics apply. It's just that there are more emergent "waves". This is the theory of generalised hydrodynamics. It is, it turns out, the right theory for quasi-one-dimensional ultracold quantum atomic gases, and also the theory for soliton gases describing certain turbulent states of (classical!) shallow water.This project will use and further expand the theory of hydrodynamics in order to evaluate exact quantities in interacting many-body systems that are otherwise inaccessible. It will use especially generalised hydrodynamics, for integrable systems, as there are many strong mathematical techniques available there, but also conventional hydrodynamics, for non-integrable systems, where the phenomenology can be very different.The theory at the basis of this project is the "ballistic fluctuation theory" (BFT), introduced by the PI and his collaborators in 2018. This gives an understanding, based solely on hydrodynamics, for how the many-body system fluctuates at very large scales of space and time. Fluctuations encode many deep properties of the system which cannot be seen just by looking at wave propagations, for instance. This theory is in effect a "dynamical" generalisation of the well-established theory of thermodynamics. The goal of the project is to first confirm the BFT and explain it to a wider audience of researchers in various fields, by comparing with computer simulations; to further develop the framework; and to extract its most non-trivial consequences.The consequences will include predictions for the decay of correlations and the growth of statistical cumulants. The exact evaluation of these quantities is a long-standing problem in many-body physics, and especially in the context of integrability. The project will also develop further the BFT by analysing the effects of diffusion and connecting with the successful, older, "macroscopic fluctuation theory"; and the effects of integrability breaking and the (quantum) Boltzmann equation.

气体和流体是由大量相互作用的粒子组成的。由于相互作用，混沌使得预测粒子的轨迹变得困难，实际上是不可能的。即使只有三个粒子，这也是真的，更不用说有很多粒子了。但是，对于大量的粒子，会出现另一种简化：如果我们忘记单独的轨迹，而是看“从远处”看时发生的事情，系统再次变得简单描述。从本质上讲，轨迹是平均的，在大的观测尺度上，出现的是更简单、更平滑的，并且由减少的有效自由度来描述。不需要知道水分子的所有轨迹来确定波是如何传播的：波动方程要简单得多。令人惊讶的是，流体力学是一套远远超出水和其他简单流体的概念：它描述了金属中的电子，现代实验中的准一维量子超冷铷原子，磁性材料中的自旋等等。事实上，更令人惊讶的是，最近发现混沌不是流体动力学发生的必要条件。对于“可积”的系统--这是一种数学性质，意味着用很少的粒子就可以完全计算出可积性，并且没有混沌--流体力学的思想仍然适用。只是有更多的紧急“波”。这就是广义流体力学理论。事实证明，它是准一维超冷量子原子气体的正确理论，也是描述（经典！）本项目将使用并进一步扩展流体力学理论，以评估相互作用的多体系统中的准确数量，否则无法获得这些数量。它将特别使用广义流体力学，用于可积系统，因为那里有许多强大的数学技术，但也有传统的流体力学，用于不可积系统，其中现象可能非常不同。该项目的基础理论是PI及其合作者在2018年提出的“弹道涨落理论”（BFT）。这给出了一个理解，仅仅基于流体力学，对于多体系统如何在非常大的空间和时间尺度上波动。波动编码了系统的许多深层性质，这些性质不能仅仅通过观察波的传播来看到。这一理论实际上是对热力学的成熟理论的“动力学”概括。该项目的目标是首先确认BFT，并通过与计算机模拟进行比较，向各个领域的更广泛的研究人员解释它;进一步发展该框架;并提取其最重要的后果，包括预测相关性的衰减和统计累积量的增长。这些量的精确计算是多体物理学中一个长期存在的问题，特别是在可积性的背景下。该项目还将通过分析扩散的影响并与成功的、较老的“宏观波动理论”相联系，以及可积性破缺和（量子）玻尔兹曼方程的影响，进一步发展BFT。