论文标题
扩展量子系统中的混乱和千古，嘈杂的驾驶
Chaos and Ergodicity in Extended Quantum Systems with Noisy Driving
论文作者
论文摘要
我们研究了一个局部量子电路家族中的时间演化运算符，其随机场朝着固定的方向。我们认为，量子混乱的存在意味着在很大程度上，进化算子在多体希尔伯特空间中有效地成为一个随机矩阵。为了量化这一现象，我们通过分析计算进化算子的痕迹的平方幅度（广义光谱形式因子）与随机矩阵理论（RMT）的预测进行了比较。我们表明，对于正在考虑的系统，可以用无限温度状态下局部可观察物的动态相关函数表示广义频谱颜色。这也提供了多体性时间之间的连接$τ_ {\ rm th} $ - 遵循随机矩阵理论预测和系统的保护定律开始的广义光谱函数开始的时间。此外，我们用系统大小来解释$τ_ {\ rm th} $的不同量表，该系统大小是针对有或没有保护定律的系统观察到的。
We study the time evolution operator in a family of local quantum circuits with random fields in a fixed direction. We argue that the presence of quantum chaos implies that at large times the time evolution operator becomes effectively a random matrix in the many-body Hilbert space. To quantify this phenomenon we compute analytically the squared magnitude of the trace of the evolution operator -- the generalised spectral form factor -- and compare it with the prediction of Random Matrix Theory (RMT). We show that for the systems under consideration the generalised spectral form factor can be expressed in terms of dynamical correlation functions of local observables in the infinite temperature state, linking chaotic and ergodic properties of the systems. This also provides a connection between the many-body Thouless time $τ_{\rm th}$ -- the time at which the generalised spectral form factor starts following the random matrix theory prediction -- and the conservation laws of the system. Moreover, we explain different scalings of $τ_{\rm th}$ with the system size, observed for systems with and without the conservation laws.
