标题： 纯态的普遍非平衡动力学以及Sachdev-Ye-Kitaev模型中的密度依赖性热化 显示英文标题

标题： Universal non-equilibrium dynamics of pure states and density-dependent thermalization in Sachdev-Ye-Kitaev model

摘要： 非平衡动力学的非纠缠和纠缠纯态在相互作用量子系统中对于利用量子信息和理解量子热化至关重要。我们开发了一种一般的施温格-凯尔迪什（SK）场理论，用于费米子纯态的非平衡动力学。我们将我们的形式应用于研究复杂萨奇德-叶-基塔耶夫（SYK）模型中初始密度不均匀性和纯态多点关联的时间演化。我们展示了SYK模型中纯态动力学的显著普遍性。我们表明，在固定粒子数部分中几乎所有纯态的动力学仅由一组通用的大-$N$卡丹诺夫-巴伊姆方程决定。此外，无论初始状态如何，位点和无序平均格林函数都会立即热化，而局部和非局部格林函数具有有限的热化率。我们通过随机矩阵理论（RMT）分析支持我们的大-$N$结果。此外，我们表明在非相互作用SYK$_2$模型中的初始纯态产品的热化与费米子填充无关，初始密度不均匀性由于去相位而以弱但长寿命的振荡衰减。相反，相互作用的SYK$_{q\geq 4}$模型比非相互作用模型热化得更慢，并表现出与填充相关的单调弛豫的初始不均匀性。对于纠缠纯态的演化，我们表明初始纠缠被编码在非局部和/或多点量子关联中，随着系统热化而弛豫。 显示英文摘要

摘要： Non-equilibrium dynamics of unentangled and entangled pure states in interacting quantum systems is crucial for harnessing quantum information and to understand quantum thermalization. We develop a general Schwinger-Keldysh (SK) field theory for non-equilibrium dynamics of pure states of fermions. We apply our formalism to study the time evolution of initial density inhomogeneity and multi-point correlations of pure states in the complex Sachdev-Ye-Kitaev (SYK) models. We demonstrate a remarkable universality in the dynamics of pure states in the SYK model. We show that dynamics of almost all pure states in a fixed particle number sector is solely determined by a set of universal large-$N$ Kadanoff-Baym equations. Moreover, irrespective of the initial state the site- and disorder-averaged Green's function thermalizes instantaneously, whereas local and non-local Green's functions have finite thermalization rate. We support our large-$N$ results through random-matrix theory (RMT) analysis. Furthermore, we show that the thermalization of an initial pure product state in the non-interacting SYK$_2$ model is independent of fermion filling and an initial density inhomogeneity decays with weak but long lived oscillations due to dephasing. In contrast, the interacting SYK$_{q\geq 4}$ model thermalizes slower than the non-interacting model and exhibits filling-dependent monotonic relaxation of initial inhomogeneity. For evolution of entangled pure states, we show that the initial entanglement is encoded in the non-local and/or multi-point quantum correlations that relax as the system thermalizes.