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Importance of the Wick rotation on Tunnelling

Amaury Mouchet
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Abstract

A continuous complex rotation of time $t\mapsto t\EXP{-iθ}$ 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 $θ=0$, is blurred out long before the Wick rotation is completed ($θ=π/2$). The influence of resonances on tunnelling rates weakens exponentially as $θ$ 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.

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Amaury Mouchet. 2007-02-01. Importance of the Wick rotation on Tunnelling. https://arxiv.org/abs/nlin/0702003

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