Many-Body Quantum Processes at the Edge of Chaos:From Non-Equilibrium Thermodynamics towards Quantum Gravity

混沌边缘的多体量子过程：从非平衡热力学到量子引力

• 批准号: 456449460
• 负责人: Professor Dr. Klaus Richter
• 金额: --
• 依托单位: Institut für Theoretische Physik
• 依托单位国家: 德国
• 项目类别: Reinhart Koselleck Projects
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/456449460?language=en
• 关键词: Many; Body; Quantum; Processes; Edge

During the recent years a novel field in theoretical physics has emerged at the interface of statistical physics, quantum dynamics in atomic and condensed matter and cosmology, which can be subsumed under the topic many-body quantum chaos. Many systems from all these distinctly different areas have in common that they reside at the semiclassical border between many-body classical chaos and quantum physics, in fact in a two-fold way: (i) Far-out-of-equilibrium quantum dynamics involves high-energy excitations, associated with the usual short-wavelength limit where wave mechanics approaches the limit of classical particles; (ii) alternatively, the thermodynamic limit of large particle numbers N, where quantum fields pass into nonlinear waves, can also be regarded as semiclassical, governed by an effective Planck constant 1/N. These two complementary crossover regimes in state-of-the-art many-body physics that are experimentally relevant and theoretically particularly challenging, are central to this proposal and form the background for two methodically intimately connected major research streams:(i) I propose to develop a theory of thermo-scattering-dynamics, i.e., to probe quantum non-equilibrium processes through scattering. Developing a fundamental relation between the density of states and the scattering time delay of open many-body systems I will be able to directly connect thermodynamic observables to microscopic dynamical scattering properties, implying for instance to measure temperature or entropy by means of scattering times. Moreover, this opens up the intriguing possibility to monitor quantum thermalization processes, or mechanisms inhibiting them such as many-body localization, from the outside. This challenging program requires a general theory for the many-body density of states of N indistinguishable interacting particles.(ii) I propose a quantum chaos approach to quantum field theory, in particular to consider quantum gravity through the lense of many-body semiclassics. I will explore how classical and quantum field theories do diverge and predict associated many-body interference phenomena. In this respect, notably, two seemingly disconnected fields in physics, quantum chaos and quantum gravity, seem to have strong common links as signaled by striking analogies. Hence, I aim at establishing a connection between topological expansions in quantum gravity (associated with "baby-universes") and periodic-orbit theory in quantum chaos, based on a dynamical mechanism for emergent geometrical structures that I conjecture. This will contribute to a cross-fertilization of these disjoint fields. During the last years my group has developed a conceptually novel platform that provides powerful many-body tools enabling us, together with international experts, to enter these uncharted territories and to address such fundamental questions that have emerged at the interface between the classical and quantum many-particle world.

近年来，在统计物理学、原子和凝聚态物质的量子动力学和宇宙学的交叉点上出现了一个理论物理学的新领域，可归入多体量子混沌。来自所有这些明显不同领域的许多系统都有一个共同点，那就是它们位于多体经典混沌和量子物理之间的半经典边界，实际上是以双重方式存在的：(i)远非平衡量子动力学涉及高能激发，与通常的短波长极限有关，其中波动力学接近经典粒子的极限；（ii）或者，大粒子数N的热力学极限，量子场进入非线性波，也可以被视为半经典，由有效普朗克常数1/N控制。这两种互补的交叉机制在实验上与最先进的多体物理相关，在理论上特别具有挑战性，是本提案的核心，并形成了两个系统密切相关的主要研究流的背景：(i)我建议发展一种热散射动力学理论，即通过散射来探索量子非平衡过程。建立开放多体系统的状态密度和散射时间延迟之间的基本关系，我将能够直接将热力学观测结果与微观动力学散射特性联系起来，例如通过散射时间来测量温度或熵。此外，这开辟了从外部监测量子热化过程或抑制它们的机制（如多体定位）的有趣可能性。这个具有挑战性的程序需要一个关于N个不可区分的相互作用粒子的多体态密度的一般理论。（ii）我提出量子场理论的量子混沌方法，特别是通过多体半经典的透镜来考虑量子引力。我将探讨经典场论和量子场论是如何分离的，并预测相关的多体干涉现象。在这方面，值得注意的是，物理学中两个看似不相关的领域，量子混沌和量子引力，似乎有很强的共同联系，正如惊人的类比所表明的那样。因此，我的目标是建立量子引力的拓扑展开（与“婴儿宇宙”相关）和量子混沌中的周期性轨道理论之间的联系，基于我推测的新兴几何结构的动力机制。这将有助于这些不相交的田地相互施肥。在过去的几年里，我的团队开发了一个概念新颖的平台，它提供了强大的多体工具，使我们能够与国际专家一起进入这些未知的领域，并解决在经典和量子多粒子世界之间的界面上出现的基本问题。