标题： 隧道效应中维克旋转的重要性 显示英文标题

标题： Importance of the Wick rotation on Tunnelling

摘要： 对时间 $t\mapsto t\EXP{-i\theta}$ 进行连续复数旋转被证明可以平滑掉混沌隧穿所特有的巨大波动。 这在受激转子模型（量子标准映射）中得到了说明，其中映射的周期被复数化：如果对于 $\theta=0$ 来说是显著的，那么与之相关的混沌经典动力学会在完成维克旋转（$\theta=\pi/2$）之前就已经变得模糊不清。 共振对隧穿率的影响随着 $\theta$ 从零开始增加而以指数方式减弱，波动越剧烈，减弱得越快。 因此，长程波动可以在无歧义的情况下以确定性的方式被识别。 当这些波动被消除后，隧穿恢复到由规则瞬时量作用支配的（准）可积指数行为。 显示英文摘要

摘要： A continuous complex rotation of time $t\mapsto t\EXP{-i\theta}$ is shown to smooth out the huge fluctuations that characterise chaotic tunnelling. This is illustrated in the kicked rotor model (quantum standard map) where the period of the map is complexified: the associated chaotic classical dynamics, if significant for $\theta=0$, is blurred out long before the Wick rotation is completed ($\theta=\pi/2$). The influence of resonances on tunnelling rates weakens exponentially as $\theta$ increases from zero, all the more rapidly the sharper the fluctuations. The long range fluctuations can therefore be identified in a deterministic way without ambiguity. When the last ones have been washed out, tunnelling recovers the (quasi-)integrable exponential behaviour governed by the action of a regular instanton.