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Edge Switching Transformations of Quantum Graphs

100%
Aizenman M., Schanz H., Smilansky U., Warzel S.
Acta Physica Polonica A
|
2017
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vol. 132
|
issue 6
1699-1703
EN
Discussed here are the effects of basics graph transformations on the spectra of associated quantum graphs. In particular it is shown that under an edge switch the spectrum of the transformed Schrödinger operator is interlaced with that of the original one. By implication, under edge swap the spectra before and after the transformation, denoted by {Eₙ}^{∞}ₙ₌₁ and {Ẽₙ}^{∞}ₙ₌₁ correspondingly, are level-2 interlaced, so that Eₙ-₂ ≤ Ẽₙ ≤ Eₙ₊₂. The proofs are guided by considerations of the quantum graphs' discrete analogs.
2
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Neutron Resonances: Widths Distribution versus the Porter-Thomas Law

76%
Sokolov V.
Acta Physica Polonica A
|
2017
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vol. 132
|
issue 6
1704-1706
EN
The neutron resonance scattering off heavy nuclei is a paradigmatic example of the chaotic processes that are well described within the framework of the standard Random Matrix Theory (RMT). In zero approximation of non-overlapping resonances, the resonance width distribution is given by the standard Porter-Thomas law (PTD) dw/dx= e^{-x/2}/√(2πx), where x=Γ/⟨Γ⟩ is the resonance width measured in the units of its mean value. We analyze the influence of the resonance overlapping and show that the experimentally observed deviations from of the PTD arise due to the influence of a moderate number of neighboring resonances located inside a restricted energy interval within which the mean level spacing D remains constant.
3
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Fluctuations and Correlations in Scattering on a Resonance Coupled to a Chaotic Background

64%
Savin D.
Acta Physica Polonica A
|
2017
|
vol. 132
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issue 6
1688-1694
EN
We discuss and briefly overview recent progress with studying fluctuations in scattering on a resonance state coupled to the background of many chaotic states. Such a problem arises naturally, e.g., when dealing with wave propagation in the presence of a complex environment. Using a statistical model based on random matrix theory, we obtain a number of nonperturbative results for various statistics of scattering characteristics. This includes the joint and marginal distributions of the reflection and transmission intensities and phases, which are derived exactly at arbitrary coupling to the background with finite absorption. The intensities and phases are found to exhibit highly non-trivial statistical correlations, which remain essential even in the limit of strong absorption. In the latter case, we also consider the relevant approximations and their accuracy. As an application, we briefly discuss the statistics of the phase rigidity (or mode complexness) in such a scattering situation.
4
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Analysis of Missing Level Statistics for Microwave Networks Simulating Quantum Chaotic Graphs Without Time Reversal Symmetry - the Case of Randomly Lost Resonances

64%
Ławniczak M., Białous M., Yunko V., Bauch S., Dietz B., Sirko L.
Acta Physica Polonica A
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2017
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vol. 132
|
issue 6
1672-1676
EN
We present experimental and numerical studies for level statistics in incomplete spectra obtained with microwave networks simulating quantum chaotic graphs with broken time reversal symmetry. We demonstrate that, if resonance frequencies are randomly removed from the spectra, the experimental results for the nearest-neighbor spacing distribution, the spectral rigidity and the average power spectrum are in good agreement with theoretical predictions for incomplete sequences of levels of systems with broken time reversal symmetry.
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