Modification of the Porter-Thomas Distribution by Rank-One Interaction

Bogomolny, E.

doi:10.1103/physrevlett.118.022501

Cited by 18 publications

(29 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore without further calculations it is physically obvious that for an interaction as in (6) and level spacings of the order of 1/N (for γ > 1) an exact eigenfunction is spread between N 2−γ levels when 1 < γ < 2 and will be fully localised when γ > 2. Notice that the exact result [20] for the case of usual random matrix models perturbed by rank-one perturbations leads to similar formulas.…”

mentioning

confidence: 70%

“…It is clear that these asymptotic values correspond to the moments of distributions (20) and (22) respectively. It is also possible to find corrections to the above results (cf.…”

mentioning

confidence: 86%

“…The main difference with the case 1 < γ < 2 is that the large x expansion (22) does not exist due to the restriction |Ψ j | ≤ 1 as has been mentioned above. Consequently, the eigenfunction distribution is given by the Cauchy expression (20) which is sharply cut at the maximal possible value (19) (which corresponds to strong localisation). It means that eigenfunction moments are given by Eq.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Eigenfunction distribution for the Rosenzweig-Porter model

Bogomolny

Sieber

2018

Phys. Rev. E

Self Cite

View full text Add to dashboard Cite

The statistical distribution of eigenfunctions for the Rosenzweig-Porter model is derived for the region where eigenfunctions have fractal behaviour. The result is based on simple physical ideas and leads to transparent explicit formulas which agree very well with numerical calculations. It constitutes a rare case where a non-trivial eigenfunction distribution is obtained in a closed form.Random matrix theory has been successfully applied to a vast number of different problems ranging from nuclear physics to number theory (see eg. [1,2] and references therein). Recently [3] it was demonstrated that it is also applicable for describing models with fractal eigenfunctions. The difference of the model considered in [3] from other models with fractal eigenfunctions, such as the power-law random banded matrices [4] and the ultrametric matrices [5], is that in the latter models fractality (or even multifractality) exits only at special critical values of the parameters, but in the former model fractality has been observed in part of the whole delocalised phase.The model in question belongs to the Rosenzweig-Porter (RP) matrix ensembles H ij [6] where all matrix elements are independent (up to the Hermitian symmetry) Gaussian variables with zero mean, and whose variances of diagonal and off-diagonal elements depend on different powers of the matrix dimension N arXiv:1804.04655v1 [quant-ph]

show abstract

mentioning

confidence: 70%

“…It is clear that these asymptotic values correspond to the moments of distributions (20) and (22) respectively. It is also possible to find corrections to the above results (cf.…”

mentioning

confidence: 86%

mentioning

confidence: 99%

See 1 more Smart Citation

Eigenfunction distribution for the Rosenzweig-Porter model

Bogomolny

Sieber

2018

Phys. Rev. E

Self Cite

View full text Add to dashboard Cite

show abstract

“…Mainly, some analytical results were obtained up to now in the limiting case of infinitely large number of resonances, [4][5][6][7]. Quite opposite, we show below that the principal influence on a chosen resonance comes from a restricted number of its near neighbors.…”

Section: Overlapping Resonancesmentioning

confidence: 98%

Neutron Resonances: Widths Distribution versus the Porter-Thomas Law

Соколов

2017

Acta Phys. Pol. A

View full text Add to dashboard Cite

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), 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.

show abstract

“…[11], it was proposed that the Thomas-Ehrman shift could be quite strong near the neutron threshold for the Pt isotopes and cause deviations from the PTD. However, Bogomolny subsequently proved that the only effect of an energy-independent real shift is to modify the secular variation of the average partial neutron width with energy [12]. The numerical results of Ref.…”

Section: Introductionmentioning

confidence: 98%

Neutron width statistics in a realistic resonance-reaction model

2018

View full text Add to dashboard Cite

A basic prediction of the statistical model of compound nucleus reactions is that the partial widths for decay into any open channel channel fluctuate according to the Porter-Thomas distribution (PTD). A recent experiment on sand p-wave neutron scattering from platinum isotopes found that the experimental s-wave partial neutron width distributions deviated substantially from the PTD. Several explanations for this finding have been proposed within the statistical model, but none has resolved this issue. Here, we review the application of a realistic resonance-reaction model to s-wave neutron scattering from 194 Pt. Our main conclusion is that the PTD provides an excellent description of the partial neutron width distribution, provided that the secular energy dependence of the average neutron width is correctly described. Within a realistic range of model parameters, there can be a near-threshold bound or virtual state of the neutron channel that changes this secular dependence from the usual √ E dependence, as proposed by Weidenmüller [1]. In this case, the use of the √ E dependence to analyze the data will lead to apparent deviations from the PTD. We discuss the limited parameter range where such a near threshold state can have a significant effect.

show abstract

Modification of the Porter-Thomas Distribution by Rank-One Interaction

Cited by 18 publications

References 21 publications

Eigenfunction distribution for the Rosenzweig-Porter model

Eigenfunction distribution for the Rosenzweig-Porter model

Neutron Resonances: Widths Distribution versus the Porter-Thomas Law

Neutron width statistics in a realistic resonance-reaction model

Contact Info

Product

Resources

About