Regensburg 2013 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 33: Poster II

DY 33.45: Poster

Donnerstag, 14. März 2013, 17:00–19:00, Poster C

Resonant tunnelling and complex paths : 1-d integrable models using normal forms — •Jérémy Le Deunff — MPIPKS, Dresden, Germany

Dynamical tunnelling, defined as a quantum phenomena which is classically forbidden (i.e. which cannot be described by the real classical solutions of the Hamilton's equations), may manifest itself through transition between different regions dynamically disconnected in the classical phase space. It is well-known that the classical nonlinear resonant chains observed in non integrable Hamiltonian systems affect by many order of magnitude the quantum observables describing tunnelling (splittings or decay rates). Here, we introduce a class of 1-d integrable Hamiltonians which reproduce main islands surrounded by (r:s) resonant chains in the phase space. We then propose a semiclassical formula for tunnelling splittings using a complex paths approach. We show that this approach leads to a good agreement with the exact numerical results and we compare with the resonance-assisted-tunnelling theory in different regimes.