Reference : Resonance- and Chaos-Assisted Tunneling
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Resonance- and Chaos-Assisted Tunneling
Schlagheck, Peter mailto [Université de Liège - ULg > Département de physique > Physique quantique statistique >]
Eltschka, C. [ > > ]
Ullmo, D. [ > > ]
Progress in Ultrafast Intense Laser Science I
Yamanouchi, K.
Chin, S. L.
Agostini, P.
Agostini, G.
[en] We consider dynamical tunneling between two symmetry-related regular
islands that are separated in phase space by a chaotic sea. Such tunneling
processes are dominantly governed by nonlinear resonances, which induce a coupling
mechanism between “regular” quantum states within and “chaotic” states
outside the islands. By means of a random matrix ansatz for the chaotic part of
the Hamiltonian, one can show that the corresponding coupling matrix element directly
determines the level splitting between the symmetric and the antisymmetric
eigenstates of the pair of islands. We show in detail how this matrix element can
be expressed in terms of elementary classical quantities that are associated with
the resonance. The validity of this theory is demonstrated with the kicked Harper

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