量子动力学与复杂性中的大偏差
Large deviations in quantum dynamics and complexity
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中文总结 AI 辅助
研究多体量子动力学中三种大偏差定义，包括可观测量全分布、测量结果分布和期望值分布。在无守恒律系统中，它们达到长时间极限的时间不同，且存在边界，其值随\(t_{\max}\)演化可度量量子复杂性。
中文摘要 AI 辅助
我们研究了多体量子动力学中三种大偏差的定义：（i）通过一个广延可观测量的全分布；（ii）通过在时间区间\(t \leq t_{\max}\)内对可观测量进行连续监测得到的测量结果分布；（iii）通过在\(t \leq t_{\max}\)内期望值的分布。在无守恒律的一般系统中，大偏差函数（i）在\(t \sim \mathcal{O}(1)\)时达到其长时间极限，与系统大小\(N\)无关。（ii）和（iii）分别在\(t \sim e^{N}\)和\(t \sim \exp(e^{N})\)时达到长时间极限。在此之前，已探索和未探索的结果/期望值之间存在一个“尖锐”边界；它们的分布等于在随\(t_{\max}\)漂移的值处截断的长时间极限。我们提出这些值随\(t_{\max}\)的演化提供了一种量子复杂性的度量。
英文摘要
We study three definitions of large deviation in many-body quantum dynamics: (i) via the full distribution of an extensive observable, (ii) via the distribution of measurement outcomes (from a continuous monitoring of the observable) over a time interval $t \le t_{\max}$, and (iii) via the distribution of expectation values over $t \le t_{\max}$. In generic systems without conservation laws, the large deviation function (i) reaches its longtime limit at $t \sim \mathcal{O}(1)$, independently of system size $N$. (ii) and (iii) reach their longtime limit at $t \sim e^{ N}$ and $t \sim \exp(e^{N})$, respectively. Before that, there is a {\it sharp} frontier between the explored and unexplored outcomes/expectation values; their distribution equals the longtime limit truncated at values that drift with $t_{\max}$. We propose that the evolution of these values with $t_{\max}$ provides a measure of quantum complexity.
