Spectral properties of strongly perturbed Coulomb systems: Fluctuation properties

Hönig, A.; Wintgen, Dieter

doi:10.1103/physreva.39.5642

Cited by 70 publications

(30 citation statements)

References 63 publications

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“…The Brody parameter can be tuned to interpolate smoothly between the limiting cases of Poisson (q 0) and Wigner (q 1) statistics, and is roughly related to the fraction of classical phase space occupied by chaotic orbits [4]. First laser experiments were carried out on diamagnetic hydrogen [6,8].…”

Section: -9007͞98͞81(22)͞4843(4)$1500mentioning

confidence: 99%

“…The Rydberg atom in a strong magnetic field is particularly suited to confront calculations with experimental results. Energy level statistics is considered to be a tool to observe a "fingerprint of chaos" in experimental spectra [1][2][3][4]. In this Letter we present experiments on diamagnetic helium Rydberg atoms in the regular and chaotic regime performed with a resolution sufficient to observe all spectral details.…”

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confidence: 99%

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Observation of the Transition to Chaos in the Level Statistics of Diamagnetic Helium

1998

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We have investigated level statistics in constant-scaled-energy spectra of the diamagnetic helium atom. In a transversely laser-cooled beam metastable triplet atoms are excited to Rydberg states in the presence of a magnetic field, resolving all resonances. In the regime of regular classical motion level distributions obeying Poisson statistics are observed. Small deviations are attributed to scattering at the nonhydrogenic He 1 core as inferred from closed-orbit theory. The nearest-neighbor spacings in spectra in the chaotic regime demonstrate a clear shift towards Wigner statistics. [S0031-9007(98)

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Section: -9007͞98͞81(22)͞4843(4)$1500mentioning

confidence: 99%

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confidence: 99%

Observation of the Transition to Chaos in the Level Statistics of Diamagnetic Helium

1998

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“…That 63 is much larger for integrable systems than chaotic ones demonstrates a tendency of the levels to bunch together in integrable systems. Systems in which the classical phase space is a mixture of chaotic and nonchaotic regions h3 stay between the two limiting curves for all values of L [5]. By using Gutzwiller's periodic orbit theory [6] and certain assumptions on how the periodic orbits of a chaotic system are distributed in phase space, Berry [7] was able to derive that in the semiclassical limit 53 statistics agree with the GOE for L «L ".…”

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confidence: 99%

Time scales of ergodic classical dynamics in quantal spectra

Arve¹

1991

Phys. Rev. A

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The 400 first energy levels of the quantal Sinai billiard has been calculated for different small central disk radii. The spectral rigidity over sequences of L levels, 63(L), agrees with that of the Gaussian orthogonal ensemble of matrices (GOE), for L & Ld. However, for larger intervals 63 exceeds that of the GOE, and increases linearly. The value of the breakpoint Ld grows with the radius, probably reflecting the increasing chaos in the classical Sinai billiard. It is suggested that in the semiclassical limit such a behavior is generic for systems with a K-mixing classical analog. PACS number(s): 05.45.+b, 03.65.Sq Bohigas, Giannoni, and Schmit conjectured in a Letter several years ago [1] that in chaotic systems, fluctuations in the density of quantal levels follow generically the Gaussian orthogonal ensemble (GOE) [2]. They demon-

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“…As experimental studies show [1,2], the main property characteristic of quantum chaos is the repulsion of quasienergy terms E n ͑͒ at those values of the parameter for which, in the case of classical consideration, there arises dynamic stochasticity. Difficulties encountered in studying quantum chaos make it necessary to pass from the quantum-mechanical description to the quantum-statistical one.…”

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Quantum-mechanical research on nonlinear resonance and the problem of quantum chaos

2004

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The quantum-mechanical investigation of nonlinear resonance in terms of approximation to moderate nonlinearity is reduced to the investigation of eigenfunctions and eigenvalues of the Mathieu-Schrodinger equation. The eigenstates of the Mathieu-Schrodinger equation are nondegenerate in a certain area of pumping amplitude values in the neighborhood of the classical separatrix. Outside this area, the system finds itself in a degenerate state for both small and large pumping amplitude values. Degenerate energy terms arise as a result of merging and branching of pairs of nondegenerate energy terms. Equations are obtained for finding the merging points of energy terms. These equations are solved by numerical methods. The main objective of this paper is to establish a quantum analog of the classical stochastic layer formed in the separatrix area. With this end in view, we consider a nonstationary quantum-mechanical problem of perturbation of the state of the Mathieu-Schrodinger equation. It is shown that in passing through the branching point the system may pass from the pure state to the mixed one. At multiple passages through branching points there develops the irreversible process of "creeping" of the system to quantum states. In that case, the observed population of a certain number of levels can be considered, in our opinion, to be a quantum analog of the stochastic layer. The number of populated levels is defined by a perturbation amplitude.

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Spectral properties of strongly perturbed Coulomb systems: Fluctuation properties

Cited by 70 publications

References 63 publications

Observation of the Transition to Chaos in the Level Statistics of Diamagnetic Helium

Observation of the Transition to Chaos in the Level Statistics of Diamagnetic Helium

Time scales of ergodic classical dynamics in quantal spectra

Quantum-mechanical research on nonlinear resonance and the problem of quantum chaos

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