论文标题
有限的lyapunov波动以及经典和量子订购的扩展率指数的上限
Finite-time Lyapunov fluctuations and the upper bound of classical and quantum out-of-time-ordered expansion rate exponents
论文作者
论文摘要
这封信证明了Chaotic Maps（逻辑，经典和量子标准图（SMS））表明，超时订购的四点相关器（OTOC）的指数增长率（$λ$）等于经典的Lyapunov指数（$λ$）\ textit {plus} $Δ^^^^^^^^^^^{一步有限的Lyapunov指数（FTLE）。 Jensen的不平等为被考虑的系统提供了上限$λ\leλ$。公平是用$λ=λ+δ^{\ mbox {\ tiny（fluc）}} $恢复的，其中$ k $ -h $ -high-higher-forder-forder-forder-rerger-rerger-rerger-rerger-rerger-forder-forters累积。使用$ k = 20 $ furnish $Δ^{\ mbox {\ tiny（fluc）}} \ sim \ ln {（\ sqrt {2}）$使用$Δ^{\ tiny（fluc）}} $ for \ textit {所有maps}（所有maps}（所有smss in smss）。
This Letter demonstrates for chaotic maps (logistic, classical and quantum standard maps (SMs)) that the exponential growth rate ($Λ$) of the out-of-time-ordered four-point correlator (OTOC) is equal to the classical Lyapunov exponent ($λ$) \textit{plus} fluctuations ($Δ^{\mbox{\tiny (fluc)}}$) of the one-step finite-time Lyapunov exponents (FTLEs). Jensen's inequality provides the upper bound $λ\leΛ$ for the considered systems. Equality is restored with $Λ= λ+ Δ^{\mbox{\tiny (fluc)}}$, where $Δ^{\mbox{\tiny (fluc)}}$ is quantified by $k$-higher-order cumulants of the FTLEs. Exact expressions for $Λ$ are derived and numerical results using $k = 20$ furnish $Δ^{\mbox{\tiny (fluc)}} \sim\ln{(\sqrt{2})}$ for \textit{all maps} (large kicking intensities in the SMs).
