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.

气体和流体由相互相互作用的大量颗粒组成。由于这种相互作用，混乱使实际上很难预测颗粒的轨迹。即使只有三个粒子，也有大量的Fortiori，这也是如此。但是，有了大量的粒子，会发生另一种简化：如果我们忘记了单个轨迹，而是看一下“从远处”看到时会发生什么，则系统再次变得易于描述。从本质上讲，轨迹的平均水平，并且在大观测量表上出现的内容更简单，更顺畅，并且通过降低的有效自由度数量来描述。为了确定波的传播方式，无需了解所有水分子的轨迹：波动方程要简单得多。这是流体动力学，波是新兴的自由度。令人难以置信的是，流体动力学是一系列想法，它超出了水和其他简单的流体：它描述了金属中的eletron磁性材料中的旋转等等。实际上，更令人惊讶的是，最近发现混乱并不需要发生混乱。对于“可集成”的系统 - 一种数学特性，暗示着几个粒子，可以完全计算轨迹，并且没有混乱 - 仍然适用流体动力学的想法。只是有更多新兴的“波浪”。这是广义流体力学的理论。事实证明，这是准二维超低量子原子气的正确理论，以及描述（经典！）浅水的某些湍流状态的孤子气体理论。此项目将使用并进一步扩展流体动力学以评估相互作用的多体系统中无法访问的精确量。它将在可集成的系统中使用特别广义的流体动力学，因为那里有许多强大的数学技术，但也有传统的流体动力学，对于非积分系统，现象学可能会大不相同。 PI及其合作者在2018年引入的“弹道波动理论”（BFT）。这仅基于流体动力学，了解多体系统在很大的时空和时间范围内如何波动。波动编码系统的许多深度属性，例如，仅通过查看波传播就看不到。该理论实际上是对热力学理论的“动态”概括。该项目的目的是首先确认BFT，并通过与计算机模拟进行比较，向各个领域的更多研究人员解释。进一步发展框架；并提取其最不平凡的后果。后果将包括对相关性衰减和统计累积物的增长的预测。这些数量的确切评估是多体物理学的长期问题，尤其是在整合性的背景下。该项目还将通过分析扩散的影响并与成功的，较旧的，宏观的波动理论相连，以进一步发展BFT；以及集成性破坏和（量子）玻尔兹曼方程的影响。