论文标题
量子混乱在复杂性几何学上
Quantum Chaos on Complexity Geometry
论文作者
论文摘要
本文解决了量子混乱中的基本长期问题，即量子混沌系统是否可以对初始条件表现出敏感性，形式直接概括了相位空间中经典混乱的概念。我们为复杂性开发了线性响应理论，并证明复杂性可以响应混乱系统初始条件的扰动而表现出指数敏感性。有两个直接的重要结果如下：i）复杂性线性响应矩阵产生了一个频谱，该频谱完全恢复了经典限制的Lyapunov指数，ii）复杂性的线性响应由超时订单相关器给出。
This article tackles a fundamental long-standing problem in quantum chaos, namely, whether quantum chaotic systems can exhibit sensitivity to initial conditions, in a form that directly generalizes the notion of classical chaos in phase space. We develop a linear response theory for complexity, and demonstrate that the complexity can exhibit exponential sensitivity in response to perturbations of initial conditions for chaotic systems. Two immediate significant results follows: i) the complexity linear response matrix gives rise to a spectrum that fully recovers the Lyapunov exponents in the classical limit, and ii) the linear response of complexity is given by the out-of-time order correlators.
