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Instantons revisited: dynamical tunnelling and resonant tunnelling

Abstract : Starting from trace formulae for the tunnelling splittings (or decay rates) analytically continued in the complex time domain, we obtain explicit semiclassical expansions in terms of complex trajectories that are selected with appropriate complex-time paths. We show how this instanton-like approach, which takes advantage of an incomplete Wick rotation, accurately reproduces tunnelling effects not only in the usual double-well potential but also in situations where a pure Wick rotation is insufficient, for instance dynamical tunnelling or resonant tunnelling. Even though only one-dimensional autonomous Hamiltonian systems are quantitatively studied, we discuss the relevance of our method for multidimensional and/or chaotic tunnelling.
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Contributor : Amaury Mouchet <>
Submitted on : Thursday, April 8, 2010 - 7:28:47 PM
Last modification on : Tuesday, April 21, 2020 - 10:29:58 AM
Document(s) archivé(s) le : Thursday, September 23, 2010 - 12:44:41 PM


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  • HAL Id : hal-00434131, version 2
  • ARXIV : 0911.4093



Jérémy Le Deunff, Amaury Mouchet. Instantons revisited: dynamical tunnelling and resonant tunnelling. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2010, 81, pp.046205. ⟨hal-00434131v2⟩



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