Hydrodynamics of quantum matter

量子物质的流体动力学

• 批准号: RGPIN-2020-05842
• 负责人: Scaffidi, Thomas
• 金额: $ 2.84万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=762713
• 关键词: Hydrodynamics; quantum; matter

Imagine preparing a set of qubits in a simple product state, and time evolving it under a given Hamiltonian which couples them. The state of the system is going to become more and more complex as entanglement is going to build up. If one wanted to store information about the system on a classical computer, the number of bits required would increase exponentially with time. Yet, after a while one expects the system to reach a thermal equilibrium, that should be describable in terms of a few macroscopic quantities, like temperature. In the field of quantum dynamics, the goal is to understand this extremely rich process, from the microsopic quantum chaos at short times, to the emergent hydrodynamics at long times. Hydrodynamics is a universal description of fluids which emerges at length and time scales much larger than those that govern microscopic, atom-level processes. While it has been useful in almost all fields of physics, its applications in solid state physics have been fairly restricted. Recently, however, important strongly correlated systems have been found which exhibit universal transport properties which cannot be explained by a single particle picture, and for which a non-perturbative approach like hydrodynamics is warranted. The opportunity provided by these systems is twofold: it enables the study of novel regimes of transport with unique properties, and it also generates exotic types of hydrodynamic theories which would not occur otherwise ``in vacuum''. My first direction is concerned with a new regime of electronic transport in which electrons behave like a viscous fluid, and for which the ubiquitous Ohm's law is replaced by the much richer Navier-Stokes equation. Interest in this regime was recently amplified by a series of experiments in 2D materials (e.g. graphene, PdCoO2). As a new Assistant Professor at the University of Toronto, I propose to make use of my previous innovations, and to further develop the theory, which will allow me to continue my deep interaction with top experimental groups in this field (Andrew Mackenzie's, Shahal Ilani's, Nobel laureate Andre Geim's), and to continue to produce new insights into this novel regime of quantum matter. Moving beyond the semiclassical regime, I will also study the dynamics of systems deep in the quantum regime by using a new formalism my collaborators and I have recently proposed. This formalism utilizes a recursion method in operator space to reveal the exponentially growing complexity of observables. It can also be used to study many-body quantum chaos at short times, and hydrodynamics at long times. This is a very exciting time. Experimental studies of hydrodynamic behavior of electrons in solids are producing new and unexpected advances every few months. With the help of NSERC funding, I look forward to building a new theory group at the University of Toronto that will explore this new frontier of condensed matter physics.

想象一下，在一个简单的乘积状态下准备一组量子位，并在一个给定的耦合哈密顿量下对其进行时间演化。随着纠缠的增加，系统的状态会变得越来越复杂。如果想在一台经典计算机上存储有关系统的信息，所需的比特数将随着时间呈指数增长。然而，在一段时间后，人们期望系统达到热平衡，这应该可以用一些宏观量来描述，比如温度。在量子动力学领域，目标是理解这个极其丰富的过程，从短时间的微观量子混沌，到长时间的涌现流体力学。流体力学是对流体的一种通用描述，它在长度和时间尺度上比那些控制微观的、原子水平过程的时间尺度要大得多。虽然它在几乎所有物理领域都很有用，但它在固态物理中的应用却相当有限。然而，最近发现了重要的强相关系统，它们表现出不能用单粒子图解释的普遍输运特性，并且需要像流体力学这样的非摄动方法。这些系统提供的机会是双重的：它使研究具有独特性质的新输运制度成为可能，它还产生了奇特类型的流体动力学理论，否则“在真空中”就不会发生。我的第一个方向是研究一种新的电子传输机制，在这种机制下，电子的行为就像一种粘性流体，普遍存在的欧姆定律被更丰富的纳维-斯托克斯方程所取代。最近在二维材料（如石墨烯、PdCoO2）中进行的一系列实验扩大了对这一机制的兴趣。作为多伦多大学的新助理教授，我建议利用我以前的创新，并进一步发展理论，这将使我能够继续与该领域的顶级实验小组（Andrew Mackenzie的，Shahal Ilani的，诺贝尔奖获得者Andre Geim的）进行深入的互动，并继续对量子物质的新制度产生新的见解。超越半经典体系，我还将使用我和我的合作者最近提出的一种新的形式主义来研究量子体系深处的系统动力学。这种形式利用运算符空间中的递归方法来揭示可观察对象的指数增长的复杂性。它也可以用于短时间内的多体量子混沌和长时间的流体力学研究。这是一个非常激动人心的时刻。固体中电子流体动力学行为的实验研究每隔几个月就会产生意想不到的新进展。在国家科学研究委员会的资助下，我期待着在多伦多大学建立一个新的理论小组，探索凝聚态物理的新前沿。