Spectral analysis of molecular resonances in erbium isotopes: Are they close to semi-Poisson?

Roy, Kamalika; Chakrabarti, Bikas K.; Chavda, N. D.; Kota, V. K. B.; Lekala, M. L.; Rampho, G. J.

doi:10.1209/0295-5075/118/46003

Cited by 12 publications

(14 citation statements)

References 54 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Though the random matrix connection of long awaited [3][4][5][6][7][8][9][10][11] sub-Wigner statistics has come up very well in the present work, however unfortunately we do not have the analytic results in the limit n → ∞. In this regard our analytic results (12,15,16) of the 2 × 2 pseudo-symmetric matrix H (9) under three probability distribution functions are encouraging as all of them give rise to sub-Wigner statistics (see Fig.…”

Section: Resultssupporting

confidence: 53%

“…Arguments relating to the random sequences [10] are found underlying p SP (s). More recently spectral analysis of molecular resonances in Erbium isotopes [11] are also found lying close to semi-Poisson distribution. Nevertheless, a random matrix connection of sub-Wigner statistics is long due, the present work is an attempt in this direction.…”

Section: Introductionmentioning

confidence: 53%

“…giving rise to intermediate statistic which is long desired [3,7]. Also it becomes semi-Poisson p SP (s) [8,11] given above, when c = 1. The distribution of eigenvalues of some of these ensembles fits well to…”

Section: Introductionmentioning

confidence: 85%

See 2 more Smart Citations

Pseudosymmetric random matrices: Semi-Poisson and sub-Wigner statistics

Kumar

Ahmed

2017

Phys. Rev. E

View full text Add to dashboard Cite

Real non-symmetric matrices may have either real or complex conjugate eigenvalues. These matrices can be seen to be pseudo-symmetric as ηM η −1 = M t , where the metric η could be secular (a constant matrix) or depending upon the matrix elements of M . Here, we construct ensembles of a large number N of pseudo-symmetric n × n (n large) matrices using N (n(n + 1)/2 ≤ N ≤ n 2 ) independent and identically distributed (iid) random numbers as their elements. Based on our numerical calculations, we conjecture that for these ensembles the Nearest Level Spacing Distributions (NLSDs: p(s)) are sub-Wigner as p abc (s) = ase −bs c (0 < c < 2) and the distributions of their eigenvalues fit well to D( ) = A[tanh{( + B)/C} − tanh{( − B)/C}] (exceptions also discussed). These sub-Wigner NLSD are encountered in Anderson metal-insulator transition and topological transitions in a Josephson junction. Interestingly, p(s) for c = 1 is called semi-Poisson and we show that it lies close to the form p(s) = 0.59sK0(0.45s 2 ) derived for the case of 2 × 2 pseudo-symmetric matrix where the eigenvalues are most aptly conditionally real: E1,2 = a ± √ b 2 − c 2 which represent characteristic coalescing of eigenvalues in PT(Parity-Time)-symmetric systems.

show abstract

Section: Resultssupporting

confidence: 53%

Section: Introductionmentioning

confidence: 53%

See 1 more Smart Citation

Pseudosymmetric random matrices: Semi-Poisson and sub-Wigner statistics

Kumar

Ahmed

2017

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…As already mentioned, experiments with ultra-cold atoms in which the interaction strength and other parameters are controlled provide the main motivation for these studies [ 61 , 62 , 63 , 64 , 65 , 80 ]. There is now a series of theoretical investigations by a Kolkata group (references [ 25 , 26 , 27 , 28 , 29 , 81 , 82 , 83 ]), and the results of these studies are briefly described in this section. These include (i) an analysis of level fluctuations using GOE and related ensembles in trapped interacting boson systems, diffuse van der Walls clusters and molecular resonances in erbium isotopes; and (ii) statistical relaxation in interaction quench dynamics of ultra-cold bosons and thermalization in isolated quantum systems.…”

Section: Random Matrix Analysis Of Weakly Interacting Trapped Bosomentioning

confidence: 99%

“…Later, a reanalysis of the same spectra was done by Mur-Petit and Molina [ 90 ] from the view point of missing resonances using RMT and concluded that the disagreement with GOE is due to the possibility of missing resonances (about 20%) in the spectrum. Going beyond these analyses, Roy et al [ 83 ] employed a large number of measures for level fluctuations and concluded from their thorough analysis that the resonances exhibit semi-Poisson characteristics. Here, below, we describe this in some detail.…”

Section: Random Matrix Analysis Of Weakly Interacting Trapped Bosomentioning

confidence: 99%

Random k-Body Ensembles for Chaos and Thermalization in Isolated Systems

Kota

Chavda

2018

Entropy

View full text Add to dashboard Cite

Abstract:Embedded ensembles or random matrix ensembles generated by k-body interactions acting in many-particle spaces are now well established to be paradigmatic models for many-body chaos and thermalization in isolated finite quantum (fermion or boson) systems. In this article, briefly discussed are (i) various embedded ensembles with Lie algebraic symmetries for fermion and boson systems and their extensions (for Majorana fermions, with point group symmetries etc.); (ii) results generated by these ensembles for various aspects of chaos, thermalization and statistical relaxation, including the role of q-hermite polynomials in k-body ensembles; and (iii) analyses of numerical and experimental data for level fluctuations for trapped boson systems and results for statistical relaxation and decoherence in these systems with close relations to results from embedded ensembles.

show abstract