Changes in Floquet-state structure at avoided crossings: Delocalization and harmonic generation

Timberlake, Todd; Reichl, L. E.

doi:10.1103/physreva.59.2886

Cited by 38 publications

(41 citation statements)

References 29 publications

(51 reference statements)

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“…In [9], avoided level crossings in a closed resonator under the influence of a driving field are studied. The results show avoided level crossings with and without permanent mixing of the wavefunctions in a similar manner as in the open resonator studied by us.…”

Section: Discussion Of the Resultsmentioning

confidence: 99%

“…It is therefore an interesting question whether or not some permanent mixing in the wavefunctions of a microwave cavity can arise. In [9], the changes in the structure of the wavefunctions at avoided crossings in a strongly driven (closed) square potential well system are studied. The avoided crossings are shown to lead, in some cases, to temporary and, in other cases, to permanent changes as a function of driving field strength.…”

Section: Introductionmentioning

confidence: 99%

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Spectroscopic studies in open quantum systems

et al. 2000

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The spectroscopic properties of an open quantum system are determined by the eigenvalues and eigenfunctions of an effective Hamiltonian H consisting of the Hamiltonian H 0 of the corresponding closed system and a non-Hermitian correction term W arising from the interaction via the continuum of decay channels. The hermitian part of H is H 0 + ℜ(W ) while the anti-hermitian part is ℑ(W ). This holds for a many-particle system as well as for a microwave resonator. The eigenvalues E R of H are complex. They are the poles of the S-matrix and provide both the energies and widths of the states. We illustrate the interplay between ℜ(H) and ℑ(H) by means of the different interference phenomena between two neighboured resonance states. Level repulsion along the real axis appears if the interaction is caused mainly by (the non-diagonal part of) ℜ(H) while a bifurcation of the widths appears if the interaction occurs mainly due to (the non-diagonal part of) ℑ(H). We then calculate the poles of the S-matrix and the corresponding wavefunctions for a rectangular microwave resonator with a scatter as a function of the area of the resonator as well as of the degree of opening to a guide. The calculations are performed by using the method of exterior complex scaling. ℜ(W ) and ℑ(W ) cause changes in the structure of the wavefunctions which are permanent, as a rule. At full opening to the lead, short-lived collective states are formed together with long-lived trapped states. The wavefunctions of the short-lived states at full opening to the lead are very different from those at small opening. The resonance picture obtained from the microwave resonator shows all the characteristic features known from the study of many-body systems in spite of the absence of two-body forces. The poles of the S-matrix determine the conductance of the resonator. Effects arising from the interplay between resonance trapping and level repulsion along the real axis are not involved in the statistical theory (random matrix theory).

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Section: Discussion Of the Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Spectroscopic studies in open quantum systems

et al. 2000

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“…A signature of this KAM-island is visible in representations of scattering wave functions in terms of Wigner functions. The avoided crossings of the Floquet quasi-energies of that system are studied in [17]. Sharp crossings of quasi-energies lead essentially only to a relabeling of the states, whereas broad crossings, in which more than two states take part, completely alter the Floquet states and increase the high harmonic generation.…”

Section: Introductionmentioning

confidence: 99%

Dynamical trapping and chaotic scattering of the harmonically driven barrier

et al. 2008

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A detailed analysis of the classical nonlinear dynamics of a single driven square potential barrier with harmonically oscillating position is performed. The system exhibits dynamical trapping which is associated with the existence of a stable island in phase space. Due to the unstable periodic orbits of the KAM-structure, the driven barrier is a chaotic scatterer and shows stickiness of scattering trajectories in the vicinity of the stable island. The transmission function of a suitably prepared ensemble yields results which are very similar to tunneling resonances in the quantum mechanical regime. However, the origin of these resonances is different in the classical regime.

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“…Their appearance allows for a wide variety of interesting, purely quantum mechanical, phenomena including chaos-assisted tunneling [2], the adiabatic exchange of eigenstate character [3], and generally provides the mechanism by which underlying classical chaos affects the dynamics of a quantum system [4]. Their existence is also responsible for perhaps the most well-known result in the field of quantum chaos, the nonPoisson statistical distribution of level spacings in "chaotic" quantum systems [5].…”

Section: Introductionmentioning

confidence: 99%

Avoided crossings in driven systems

Holder

Reichl

2005

Phys. Rev. A

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We characterize the avoided crossings in a two-parameter, time-periodic system which has been the basis for a wide variety of experiments. By studying these avoided crossings in the near-integrable regime, we are able to determine scaling laws for the dependence of their characteristic features on the non-integrability parameter. As an application of these results, the influence of avoided crossings on dynamical tunneling is described and applied to the recent realization of multiple-state tunneling in an experimental system.

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Changes in Floquet-state structure at avoided crossings: Delocalization and harmonic generation

Cited by 38 publications

References 29 publications

Spectroscopic studies in open quantum systems

Spectroscopic studies in open quantum systems

Dynamical trapping and chaotic scattering of the harmonically driven barrier

Avoided crossings in driven systems

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