Spectral fluctuation and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:msup><mml:mi>f</mml:mi><mml:mi>α</mml:mi></mml:msup></mml:mrow></mml:math>noise in the energy level statistics of interacting trapped bosons

Roy, Kamalika; Chakrabarti, Bikas K.; Biswas, Anindya; Kota, V. K. B.; Haldar, Sudip Kumar

doi:10.1103/physreve.85.061119

Cited by 6 publications

(18 citation statements)

References 51 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Later the theorem was verified in a more real physical quantum system [55]. Very recently we have also observed the Shnirelman peak in the level spacing distribution for three interacting bosons in the external harmonic trap [56]. In the noninteracting limit, the external trap should exhibit the exact degeneracy; however, due to the presence of a small two-body interaction in the three-boson system, the exact degeneracy is removed and the quasidegeneracy is left.…”

Section: Statistical Tools and Numerical Resultsmentioning

confidence: 95%

Energy-level statistics of interacting trapped bosons

et al. 2012

Self Cite

View full text Add to dashboard Cite

It is a well-established fact that statistical properties of energy-level spectra are the most efficient tool to characterize nonintegrable quantum systems. The statistical behavior of different systems such as complex atoms, atomic nuclei, two-dimensional Hamiltonians, quantum billiards, and noninteracting many bosons has been studied. The study of statistical properties and spectral fluctuations in interacting many-boson systems has developed interest in this direction. We are especially interested in weakly interacting trapped bosons in the context of Bose-Einstein condensation (BEC) as the energy spectrum shows a transition from a collective nature to a single-particle nature with an increase in the number of levels. However this has received less attention as it is believed that the system may exhibit Poisson-like fluctuations due to the existence of an external harmonic trap. Here we compute numerically the energy levels of the zero-temperature many-boson systems which are weakly interacting through the van der Waals potential and are confined in the three-dimensional harmonic potential. We study the nearest-neighbor spacing distribution and the spectral rigidity by unfolding the spectrum. It is found that an increase in the number of energy levels for repulsive BEC induces a transition from a Wigner-like form displaying level repulsion to the Poisson distribution for P (s). It does not follow the Gaussian orthogonal ensemble prediction. For repulsive interaction, the lower levels are correlated and manifest level-repulsion. For intermediate levels P (s) shows mixed statistics, which clearly signifies the existence of two energy scales: external trap and interatomic interaction, whereas for very high levels the trapping potential dominates, generating a Poisson distribution. Comparison with mean-field results for lower levels are also presented. For attractive BEC near the critical point we observe the Shnirelman-like peak near s = 0, which signifies the presence of a large number of quasidegenerate states.

show abstract

Section: Statistical Tools and Numerical Resultsmentioning

confidence: 95%

Energy-level statistics of interacting trapped bosons

et al. 2012

Self Cite

View full text Add to dashboard Cite

show abstract

“…It has already been pointed out in several earlier works that N interacting trapped bosons is a highly complex system [18,19]. The complexity arises due to the existence of two energy scales: one is the external trap, which is characterized by trap energy ∼ ω (ω is the external trap frequency) and the other one is the interatomic interaction energy characterized by Na s , where N is the number of bosons in the trap and a s is the s-wave scattering length.…”

Section: Introductionmentioning

confidence: 97%

“…It is known that a system of N noninteracting atoms in 3D external harmonic trap is exactly solvable and exhibits exact degeneracy. Whereas, switching the interaction gradually moves the system from integrability to nonintegrability with increase in number of bosons [18,19]. Here we are interested in the situation with weakly interacting atoms, which lift the exact degeneracy exhibiting the quasidegeneracy [18] and shows that P (s) will be a sum of δ functions [11].…”

Section: Introductionmentioning

confidence: 98%

“…Whereas, switching the interaction gradually moves the system from integrability to nonintegrability with increase in number of bosons [18,19]. Here we are interested in the situation with weakly interacting atoms, which lift the exact degeneracy exhibiting the quasidegeneracy [18] and shows that P (s) will be a sum of δ functions [11]. Although this situation is close to the earlier study of P (s) distribution of rectangular billiards [10] with aspect ratio α close to a rational number [10], our system is different, realistic, and interesting for various reasons.…”

Section: Introductionmentioning

confidence: 98%

See 1 more Smart Citation

Statistical properties of spectral fluctuations ofNinteracting bosons in a harmonic trap

Roy¹,

Chakrabarti

Kota

2014

Phys. Rev. E

Self Cite

View full text Add to dashboard Cite

Spectral fluctuations of a system of N weakly interacting bosons in an isotropic harmonic trap are studied, with the focus on the deviations from Poisson spectral statistics, typical of a quantum integrable systems. We have utilized the ideas formulated by Makino et al. [Phys. Rev. E 67, 066205 (2003)1063-651X10.1103/PhysRevE.67.066205] who have extended the approach of Berry and Robnik [J. Phys. A 17, 2413 (1984)JPHAC50305-447010.1088/0305-4470/17/12/013]. Earlier investigations of the Berry conjecture [Proc. R. Soc. London, Ser. A 356, 375 (1977)1364-502110.1098/rspa.1977.0140] of Poisson spectral statistics mainly considered quantum systems whose classical counterparts are integrable. However, the system of N weakly interacting bosons in the external trap has no classical counterpart. Also, it is a realistic and experimentally achievable system with close relation to Bose-Einstein condensation. Thus, a stringent analysis of the applicability of the Berry conjecture to this kind of systems is indeed required. We observe that for small boson number, the system is close to integrability and the nearest-neighbor level spacing distribution and the level number variance exhibit deviations from Poisson statistics similar to those of rational rectangular billiards.

show abstract

“…Also some attempts have been made for non-interacting many-bosons and interacting bosonic system [17][18][19][20]. Recently we have reported the level spacing distribution of ultra-cold interacting bosons trapped in a harmonic potential [21][22][23]. We found intriguing effect of both the interatomic interaction and the trap and observed deviation from the BGS cojecture.…”

Section: Introductionmentioning

confidence: 88%

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

Haldar¹,

Chakrabarti²,

Chavda

et al. 2014

Phys. Rev. A

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Spectral fluctuation and1/fαnoise in the energy level statistics of interacting trapped bosons

Cited by 6 publications

References 51 publications

Energy-level statistics of interacting trapped bosons

Energy-level statistics of interacting trapped bosons

Statistical properties of spectral fluctuations ofNinteracting bosons in a harmonic trap

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

Contact Info

Product

Resources

About