论文标题
多体量子混乱中普遍性的半经典根源
Semiclassical roots of universality in many-body quantum chaos
论文作者
论文摘要
多体系统的量子混乱一直在各个学科之间的界面上迅速发展成一个充满活力的研究领域，从统计物理学到凝结物质到量子信息和宇宙学。在具有经典极限的量子系统中，高级半经典方法在量子级别上提供了经典混乱的动力学与相应的通用特征之间的关键联系。最近，在通常的半经典限制$ \ hbar \ hbar \ rightarrow 0 $中，在类似半经典的半经典限制$ \ hbar_ {eff} = 1/n \ firstarrow量中的单粒子技术已经开始转变为N粒子系统的现场理论域，以实现许多$ contry contry，以销售很多$ contry，以实现许多量的量子，以实现许多量的量子，以实现许多量的量。这种半古老的多体理论提供了一个统一的框架，用于理解单粒子和多体量子混沌系统的随机矩阵相关性。某些编织的古典轨道和平均野外模式分别控制干扰，并为普遍性的基础提供了关键。介绍的案例研究包括用于光谱密度和超阶相关器的Gutzwiller的痕量公式的多体版本，以及有关进一步进展的简短评论。
Quantum chaos of many-body systems has been swiftly developing into a vibrant research area at the interface between various disciplines, ranging from statistical physics to condensed matter to quantum information and to cosmology. In quantum systems with a classical limit, advanced semiclassical methods provide the crucial link between classically chaotic dynamics and corresponding universal features at the quantum level. Recently, single-particle techniques dealing with ergodic wave interference in the usual semiclassical limit $\hbar \rightarrow 0$ have begun to be transformed into the field theoretical domain of N-particle systems in the analogous semiclassical limit $\hbar_{eff} = 1/N \rightarrow 0$, thereby accounting for genuine many-body quantum interference. This semiclassical many-body theory provides a unified framework for understanding random-matrix correlations of both single-particle and many-body quantum chaotic systems. Certain braided bundles of classical orbits, and of mean field modes, govern interference, respectively, and provide the key to the foundation of universality. Case studies presented include a many-body version of Gutzwiller's trace formula for the spectral density and out-of-time-order correlators along with brief remarks on where further progress may be forthcoming.
