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Progress in Ultrafast Intense Laser Science Volume I pp 107–131Cite as

Resonance- and Chaos-Assisted Tunneling

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Part of the book series: Springer Series in Chemical Physics ((PUILS,volume 84))

Summary

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 model.

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Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Regensburg, 93040, Regensburg, Germany

    Peter Schlagheck & Christopher Eltschka

  2. Department of Physics, Duke University, Durham, NC, USA

    Denis Ullmo

  3. CNRS, Université Paris-Sud, LPTMS, UMR 8626, 91405, Orsay Cedex, France

    Denis Ullmo

Authors
  1. Peter Schlagheck
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  2. Christopher Eltschka
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  3. Denis Ullmo
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Schlagheck, P., Eltschka, C., Ullmo, D. (2006). Resonance- and Chaos-Assisted Tunneling. In: Progress in Ultrafast Intense Laser Science Volume I. Springer Series in Chemical Physics, vol 84. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-34422-5_7

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