论文标题
连接光谱形式的流体动力学理论
Hydrodynamic Theory of the Connected Spectral Form Factor
论文作者
论文摘要
量子混乱的一种表现是一种随机的基质样细粒能谱。在逆级间隔时间之前，随机矩阵理论预测了光谱形式相互连接部分变化增加的“坡道”。然而，在现实的量子混沌系统中，光谱外形的有限时间动力学要富裕得多，纯随机矩阵坡道仅在足够的较晚时间出现。在本文中，我们提出了在逆级间隔时间之前的连接光谱符号的流体动力学理论。我们从讨论确切的对称性和光谱拉伸和折叠的讨论开始。然后，我们在每个部门内的回报概率和光谱形式方面得出了具有几乎保存部门的系统光谱形式的一般公式。接下来，我们认为波动流体动力学的理论可以从通常的schwinger-keldysh轮廓调整为光谱形式所需的周期性时间设置，并且我们明确地表明，在能量扩散的情况下，恢复了一般公式。我们还启动了对这个改良的流体动力框架的相互作用效应的研究，并展示了如何将其定义为接近纯随机矩阵结果所需的时间，该时间由缓慢的流体动力学模式控制。
One manifestation of quantum chaos is a random-matrix-like fine-grained energy spectrum. Prior to the inverse level spacing time, random matrix theory predicts a `ramp' of increasing variance in the connected part of the spectral form factor. However, in realistic quantum chaotic systems, the finite time dynamics of the spectral form factor is much richer, with the pure random matrix ramp appearing only at sufficiently late time. In this article, we present a hydrodynamic theory of the connected spectral form factor prior to the inverse level spacing time. We start from a discussion of exact symmetries and spectral stretching and folding. We then derive a general formula for the spectral form factor of a system with almost-conserved sectors in terms of return probabilities and spectral form factors within each sector. Next we argue that the theory of fluctuating hydrodynamics can be adapted from the usual Schwinger-Keldysh contour to the periodic time setting needed for the spectral form factor, and we show explicitly that the general formula is recovered in the case of energy diffusion. We also initiate a study of interaction effects in this modified hydrodynamic framework and show how the Thouless time, defined as the time required for the spectral form factor to approach the pure random matrix result, is controlled by the slow hydrodynamics modes.
