Scarring and the Statistics of Tunnelling

Creagh, Stephen C.; Lee, Sang Yup; Whelan, Niall D.

doi:10.1006/aphy.2001.6202

Cited by 16 publications

(34 citation statements)

References 35 publications

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“…The map (1) is chaotic on the unit torus [0,1[×[0,1[, and has a fixed point at the origin, where the quantum dynamics exhibits scarring effects [20]. We set = 0.1 for all the simulations that follow.…”

Section: A Modelmentioning

confidence: 99%

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On-manifold localization in open quantum maps

et al. 2012

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A quantized chaotic map exhibiting localization of wave function intensity is opened. We investigate how such patterns as scars in the Husimi distributions are influenced by the losses through a number of numerical experiments. We find the scars to relocate on the stable or unstable manifolds depending on the position of the opening, and provide a classical argument to explain the observations. For asymmetrically introduced openings mode interaction contributes to determine the localization patterns. We finally show examples of similar localization in a simulated dielectric microcavity.

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Section: A Modelmentioning

confidence: 99%

“…The closed quantum map (20) is scarred at the origin [ Fig. 7(a)], a fixed point of the classical dynamics.…”

Section: Toward a Dielectric Microcavitymentioning

confidence: 99%

On-manifold localization in open quantum maps

et al. 2012

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“…by which, in principle, the spectrum should follow COE statistics [29,30]. The quantization of the map is given by [28,31]…”

Section: Numerical Testsmentioning

confidence: 99%

“…Next, scarring is considered: the wavepackets representing opening and probe states are both centered at the origin, where the fixed point is. Here, the autocorrelation function A(t) is approximated by the semiclassical expression [26,29] A p (t) = e i arctan Q sinh λt…”

Section: Numerical Testsmentioning

confidence: 99%

Estimating the spectral density of unstable scars

Lippolis

2021

Preprint

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In quantum chaos, spectral statistics generally follows the predictions of Random Matrix Theory (RMT). A notable exception is given by scar states, that enhance probability density around unstable periodic orbits of the classical system, therefore causing significant deviations of the spectral density from RMT expectations. In this work, the problem is considered of both RMT-ruled and scarred chaotic systems coupled to an opening. In particular, predictions are derived for the spectral density of a chaotic Hamiltonian scattering into a single-or multiple channels. The results are tested on paradigmatic quantum chaotic maps on a torus. The present report develops the intuitions previously sketched in [D. Lippolis, EPL 126 (2019) 10003].

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“…built to follow the instanton trajectory. Creagh and Whelan have shown how to explicitly build such a wavepacket [23]. For a quantum chaotic system, the simplest model for describing the statistical properties of the energy spectrum and eigenstates is to use Random Matrix Theory (RMT) [16,17].…”

Section: Fluctuations Of the Ionization Rates -Effect Of Scarringmentioning

confidence: 99%

Experimentally attainable example of chaotic tunneling: The hydrogen atom in parallel static electric and magnetic fields

Delande

Zakrzewski

2003

Phys. Rev. A

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Statistics of tunneling rates in the presence of chaotic classical dynamics is discussed on a realistic example: a hydrogen atom placed in parallel uniform static electric and magnetic fields, where tunneling is followed by ionization along the fields direction. Depending on the magnetic quantum number, one may observe either a standard Porter-Thomas distribution of tunneling rates or, for strong scarring by a periodic orbit parallel to the external fields, strong deviations from it. For the latter case, a simple model based on random matrix theory gives the correct distribution.

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Scarring and the Statistics of Tunnelling

Cited by 16 publications

References 35 publications

On-manifold localization in open quantum maps

On-manifold localization in open quantum maps

Estimating the spectral density of unstable scars

Experimentally attainable example of chaotic tunneling: The hydrogen atom in parallel static electric and magnetic fields

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