We study the universal structure of late-time ensembles obtained from unitary dynamics in quantum chaotic systems with symmetries, such as charge or energy conservation. We find that although quantum states do not ergodically explore the entire Hilbert space at late times, the late-time ensemble typically becomes indistinguishable from Haar-random states in the thermodynamic limit at the level of finite statistical moments. Importantly, our results apply to initial states easy to prepare in ongoing experiments -- specifically, product states -- that lie in the middle of the spectrum of quantum chaotic systems. We show that these states typically exhibit not only the same late-time ensemble average as Haar-random states, but also the same state-to-state fluctuations and higher statistical moments. In other words, there is no measurement -- whether local or nonlocal -- at the level of finite statistical moments that can tell that the states are not exploring the entire Hilbert space. Interestingly, within the class of low-entanglement initial states, we also find atypical initial conditions in the middle of the spectrum of Hamiltonians known to be "maximally chaotic". Such atypical states have smaller variance of the symmetry operator than Haar-random states and evolve into non-universal ensembles that can be distinguished from the Haar ensemble by simple measurements or subsystem properties. In the limiting case of initial states with negligible variance of the symmetry operator (e.g., states with fixed particle number or energy eigenstates), the late-time ensemble has universal behavior captured by constrained random-state ensembles. Our results reveal that an extremely high level of quantum state randomness can still be achieved even when dynamics is constrained by symmetries.
Capacitance and charge relaxation resistance of chaotic cavities - Joint distribution of two linear statistics in the Laguerre ensemble of random matrices
Statistical complexity and the road to equilibrium in many-body chaotic quantum systems
在这项工作中，我们重新审视孤立的多体相互作用量子系统的平衡问题。我们特别关注量子混沌哈密顿量，而不是专注于渐近状态的性质以及它们如何坚持本征态热化假设的预测，我们专注于平衡过程本身，即，\emph{the road to equilibrium}。沿着平衡的对角线合奏服从紧急形式的热力学第二定律，我们提供了一个信息理论证明这一事实。有了这个证据，我们表明，通往均衡的道路只不过是一个对角合奏时间的层次结构。此外，引入统计复杂性和熵复杂性平面的概念，我们调查的唯一性的道路在一个通用的多体系统的平衡，通过比较其轨迹在熵复杂性平面的随机哈密顿产生的。最后，通过将随机哈密顿量作为扰动，我们分析了与混沌哈密顿量和不同类型的初始状态的平衡之路相关联的熵复杂性轨迹的稳定性。
Diagnosing chaos with projected ensembles of process tensors
Trinity College Dublin（都柏林三一学院）；Universität zu Köln（科隆大学）；Institut für Theoretische Physik, Universität zu Köln（科隆大学理论物理研究所）；Monash University（蒙纳士大学）；Singapore University of Technology and Design（新加坡科技设计大学）；King’s College London（伦敦国王学院）
Emergent quantum state designs and biunitarity in dual-unitary circuit dynamics
最近的工作研究了量子猝灭后酉动力学中一种新的随机矩阵行为的出现。从一个时间演化的状态开始，可以通过对系统的其余部分进行投影测量来生成一个小子系统上支持的纯态系综，从而得到一个投影系综。在混沌量子系统中，这种投影系综变得与均匀的Haar随机系综不可区分，并导致量子态设计。最近Ho和Choi [Phys. Rev. Lett. 128，060601（2022）]在自对偶点处的踢击伊辛模型。我们提供了一个替代的建设，可以扩展到一般的混沌双酉电路与可解的初始状态和测量，突出了潜在的双酉的作用，并进一步显示如何双酉电路模型表现出精确的可解性和随机矩阵行为。从双酉连接的结果的基础上，我们展示了如何复杂的阿达玛矩阵和酉误差基地都导致可解的测量方案。
