Instantons re-examined: Dynamical tunneling and resonant tunneling
Abstract
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.
- Publication:
-
Physical Review E
- Pub Date:
- April 2010
- DOI:
- 10.1103/PhysRevE.81.046205
- arXiv:
- arXiv:0911.4093
- Bibcode:
- 2010PhRvE..81d6205L
- Keywords:
-
- 05.45.Mt;
- 03.65.Sq;
- 03.65.Xp;
- 05.60.Gg;
- Quantum chaos;
- semiclassical methods;
- Semiclassical theories and applications;
- Tunneling traversal time quantum Zeno dynamics;
- Quantum transport;
- Quantum Physics;
- Nonlinear Sciences - Chaotic Dynamics
- E-Print:
- Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 81 (2010) 046205