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Resonance- and Chaos-Assisted Tunneling

  • Peter Schlagheck
  • Christopher Eltschka
  • Denis Ullmo
Part of the Springer Series in Chemical Physics book series (CHEMICAL, 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.

Keywords

Phase Space Tunneling Process Tunneling Rate Nonlinear Resonance Classical Phase Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Peter Schlagheck
    • 1
  • Christopher Eltschka
    • 1
  • Denis Ullmo
    • 2
    • 3
  1. 1.Institut für Theoretische PhysikUniversität RegensburgRegensburgGermany
  2. 2.Department of PhysicsDuke UniversityDurhamUSA
  3. 3.CNRSUniversité Paris-Sud, LPTMS, UMR 8626Orsay CedexFrance

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