Open quantum systems and random matrix theory

Mulhall, Declan

doi:10.1103/physrevc.91.014305

Cited by 5 publications

(3 citation statements)

References 21 publications

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“…In particular, width fluctuations govern the decay law [8,9] and give rise to nonorthogonal modes [10,11] leading to enhanced sensitivity to perturbations [12]. Various aspects of lifetime and width statistics are a subject of intensive research, both theoretically and experimentally, with recent studies motivated by practical applications including optical microresonators [13], superconductor superlattices [14], many-body fermionic systems [15], microwave billiards [16,17], and dissipative quantum maps [18,19], as well as by long-standing interest in superradiance-like "resonance trapping" phenomena [4,15,[20][21][22]. Recent advances in experimental techniques have made it possible to test many of theoretical predictions with unprecedented accuracy [23][24][25][26][27][28][29][30], giving further impetus for the theory development.…”

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confidence: 99%

Resonance width distribution in RMT: Weak-coupling regime beyond Porter-Thomas

Fyodorov¹,

Savin²

2015

EPL

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-We employ the random matrix theory (RMT) framework to revisit the distribution of resonance widths in quantum chaotic systems weakly coupled to the continuum via a finite number M of open channels. In contrast to the standard first-order perturbation theory treatment we do not a priory assume the resonance widths being small compared to the mean level spacing. We show that to the leading order in weak coupling the perturbative χ 2 M distribution of the resonance widths (in particular, the Porter-Thomas distribution at M = 1) should be corrected by a factor related to a certain average of the ratio of square roots of the characteristic polynomial ('spectral determinant') of the underlying RMT Hamiltonian. A simple single-channel expression is obtained that properly approximates the width distribution also at large resonance overlap, where the Porter-Thomas result is no longer applicable.Introduction.-Scattering of both classical and quantum waves in systems with chaotic intrinsic dynamics is characterised by universal statistical properties [1][2][3]. Those can be understood by studying the properties of quasi-stationary states in an open system formed at the intermediate stage of the scattering process [4][5][6][7]. Such states are associated with the resonances which correspond to the complex poles E n = E n −

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confidence: 99%

Resonance width distribution in RMT: Weak-coupling regime beyond Porter-Thomas

Fyodorov¹,

Savin²

2015

EPL

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“…In recent years, the statistical properties of different structures [1] are described by randommatrix theory (RMT). RMT has been generally used in various effective systems, such as the medical application [2][3][4], the atmosphere [1], the biological networks [5,6], the quantum graphs [7], and various other model networks [8][9][10][11][12]. The characterization of cognitive brain states [13,14] is the last application of RMT in biological sciences.…”

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confidence: 99%

Chaos and regularity of radionuclides with maximum likelihood estimation method

et al. 2020

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In this study, we considered the fluctuation properties of some energy levels of even and odd mass radionuclides, which are used in complex phenomena. Different sequences are prepared by using all the available experimental data and analyzed by using the maximum likelihood estimation technique to get the chaoticity parameter of Abul-magd distribution. The dependence of chaoticity degrees of different radionuclides to their mass regions, their decay modes, and also their physical half-lives are studied. Our results show more chaotic behavior of odd-mass radionuclides in comparison with even–even mass and also the most Poisson-like behavior for even–even mass in the A > 150 mass region. The results offer the most regular behavior for long-lived, even mass radionuclides in comparison to other categories of half-lives. Also, we got an obvious difference between the chaoticity degrees for nuclei which undergo β + decay in comparison with radionuclides which show electron capture mode.

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“…Moreover, subsequent analyses [7,8] of the reduced neutron widths in the nuclear data ensemble seem to overturn the long held belief that it furnishes persuasive evidence for the applicability of the Gaussian orthogonal ensemble (GOE) of Hamiltonian matrices [9] in the description of CN fluctuation properties. There have been several attempts to reconcile these new findings with the standard statistical models of CN processes [10][11][12][13][14][15][16][17][18][19][20][21][22], but there is a consensus [23][24][25] that more data is needed to guide theoretical considerations.…”

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confidence: 99%

Test of the Porter-Thomas distribution with the total cross section autocorrelation function

Davis

2018

Preprint

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On the basis of experiments conducted in the 1970s and earlier, it is believed that, in a compound nucleus (CN), fluctuations in transition strengths are drawn from a Porter-Thomas distribution (PTD), a χ 2 distribution of one degree of freedom. However, work done post-1990 at the Los Alamos Neutron Science Center (LANSCE) and Oak Ridge Electron Linear Accelerator (ORELA) facilities has yielded instances of neutron resonance data sets of superior quality that are inconsistent with the PTD. In view of the importance of the status of the PTD to the foundations of statistical reaction theory, the question arises whether other data acquired at these facilities can be mined for evidence of deviations from the PTD? To date, the focus has been on data taken in the regime of isolated resonances. In this letter, arguments are put forward in support of the analysis of measurements of the total cross section in the regime where resonances are weakly overlapping.

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Open quantum systems and random matrix theory

Cited by 5 publications

References 21 publications

Resonance width distribution in RMT: Weak-coupling regime beyond Porter-Thomas

Resonance width distribution in RMT: Weak-coupling regime beyond Porter-Thomas

Chaos and regularity of radionuclides with maximum likelihood estimation method

Test of the Porter-Thomas distribution with the total cross section autocorrelation function

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