Spectral fluctuation and correlation structure of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>δ</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:math>statistics in the spectra of interacting trapped bosons

Roy, Kamalika; Chakrabarti, Bikas K.; Kota, V. K. B.

doi:10.1103/physreve.87.062101

Cited by 2 publications

(2 citation statements)

References 43 publications

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“…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%

“…Finally, measures for higher-order correlations in spectral fluctuations are also studied. For 5000 bosons and focusing on the lowest 100 levels, the q -th order correlation function

was calculated for

using a two-fold averaging [ 82 ]. The numerical results clearly show that the level fluctuations follow GOE random matrix predictions, even for higher orders, i.e., a logarithmic correlation structure is seen instead of a multi-scaling structure in the

results.…”

Section: Random Matrix Analysis Of Weakly Interacting Trapped Bosomentioning

confidence: 99%

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

Kota

Chavda

2018

Entropy

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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.

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Section: Random Matrix Analysis Of Weakly Interacting Trapped Bosomentioning

confidence: 99%

“…Finally, measures for higher-order correlations in spectral fluctuations are also studied. For 5000 bosons and focusing on the lowest 100 levels, the q -th order correlation function

was calculated for

results.…”

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

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Level-spacing statistics and spectral correlations in diffuse van der Waals clusters

Haldar¹,

Chakrabarti²,

Chavda

et al. 2014

Phys. Rev. A

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We present a statistical analysis of eigenenergies and discuss several measures of spectral fluctuations and spectral correlations for the van der Waals clusters of different sizes. We show that the clusters become more and more complex with increase in cluster size. We study nearest-neighbour level spacing distribution P (s), the level number variance Σ 2 (L), and the Dyson-Mehta ∆3−statistics for various cluster sizes. For large clusters we find that although the Bohigas-Giannoni-Schmit (BGS) conjecture seems to be valid, it does not exhibit true signatures of quantum chaos. However contrasting conjecture of Berry and Tabor is observed with smaller cluster size. For small number of bosons, we observe the existence of large number of quasi-degenerate states in low-lying excitation which exhibits the Shnirelman peak in P (s) distribution. We also find a narrow region of intermediate spectrum which can be described by semi-Poisson statistics whereas the higher levels are regular and exhibit Poisson statistics. These observations are further supported by the analysis of the distribution of the ratio of consecutive level spacings P (r) which is independent of unfolding procedure and thereby provides a tool for more transparent comparison with experimental findings than P (s). Thus our detail numerical study clearly shows that the van der Waals clusters become more correlated with the increase in cluster size.

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Spectral fluctuation and correlation structure ofδnstatistics in the spectra of interacting trapped bosons

Cited by 2 publications

References 43 publications

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

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

Level-spacing statistics and spectral correlations in diffuse van der Waals clusters

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