[en] Resonance-assisted tunneling is investigated within the framework of one-dimensional integrable systems. We present a systematic recipe, based on Hamiltonian normal forms, to construct one-dimensional integrable models that exhibit resonance island chain structures with accurately controlled sizes and positions of the islands. Using complex classical trajectories that evolve along suitably defined paths in the complex time domain, we construct a semiclassical theory of the resonance-assisted tunneling process. This semiclassical approach yields a compact analytical expression for tunnelling-induced level splittings which is found to be in very good agreement with the exact splittings obtained through numerical diagonalization.
Disciplines :
Physics
Author, co-author :
Le Deunff, Jérémy
Mouchet, Amaury
Schlagheck, Peter ; Université de Liège - ULiège > Département de physique > Physique quantique statistique
Language :
English
Title :
Semiclassical description of resonance-assisted tunneling in one-dimensional integrable models
Publication date :
2013
Journal title :
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
ISSN :
1539-3755
eISSN :
1550-2376
Publisher :
American Physical Society, College Park, United States - Maryland
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