Instantons re-examined: dynamical tunneling and resonant tunneling.
Starting from trace formulas for the tunneling 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 instantonlike approach, which takes advantage of an incomplete Wick rotation, accurately reproduces tunneling effects not only in the usual double-well potential but also in situations where a pure Wick rotation is insufficient, for instance dynamical tunneling or resonant tunneling. Even though only one-dimensional autonomous Hamiltonian systems are quantitatively studied, we discuss the relevance of our method for multidimensional and/or chaotic tunneling.
Le Deunff
Jérémy
J
Laboratoire de Mathématiques et de Physique Théorique, Université François Rabelais de Tours-CNRS, Fédération Denis Poisson, UMR 6083, Parc de Grandmont, 37200 Tours, France. jeremy.ledeunff@lmpt.univ-tours.fr
Mouchet
Amaury
A