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

近年来，在统计物理、原子与凝聚态的量子动力学和宇宙学的界面上出现了一个新的理论物理领域，这个领域可以归入多体量子混沌这一主题。来自所有这些截然不同领域的许多系统都有一个共同点，它们位于多体经典混沌和量子物理之间的半经典边界，实际上是以两种方式：(I)远超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，其中量子场进入非线性波，也可以被认为是半经典的，由有效的普朗克常数1/N决定。在最先进的多体物理中，这两个互补的交叉制度在实验上是相关的，在理论上特别具有挑战性，是这一提议的核心，并构成了两个有条不紊地密切联系的主要研究流的背景：(I)我提议发展一个热散射动力学理论，即通过散射来探索量子非平衡过程。发展开放多体系统的态密度和散射时滞之间的基本关系我将能够直接将热力学观察值与微观动态散射性质联系起来，这意味着例如通过散射时间来测量温度或熵。此外，这为从外部监测量子热化过程或抑制它们的机制(如多体定域化)提供了有趣的可能性。这一具有挑战性的计划需要一个关于N个不可区分相互作用粒子的多体密度的一般理论。(Ii)我提出了量子混沌方法来研究量子场论，特别是通过多体半经典的透镜来考虑量子引力。我将探索经典理论和量子场理论是如何发散的，并预测相关的多体干涉现象。在这方面，值得注意的是，物理学中的两个看似互不关联的领域--量子混沌和量子引力--似乎有很强的共同联系，这一点从惊人的类比中可见一斑。这将有助于这些不相交的田地的交叉施肥。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领域，并解决在经典和量子多粒子世界之间出现的基本问题。

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.