Friday, February 3, 2012

1101.5469 (Barnali Chakrabarti et al.)

Spectral statistics of interacting trapped many-boson systems in 3D    [PDF]

Barnali Chakrabarti, Anindya Biswas, V. K. B. Kota, Kamalika Roy, Sudip Kumar Haldar
It is an well established fact that statistical properties of energy level
spectra are the most efficient tool to characterize nonintegrable quantum
systems. The study of statistical properties and spectral fluctuation in the
interacting many boson systems have developed a new interest in this direction.
Specially we are interested in the weakly interacting trapped bosons in the
context of Bose-Einstein condensation (BEC) as the energy spectrum shows a
transition from the collective to single particle nature with the 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 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 in the 3D confined harmonic
potential. We study the nearest neighbour spacing distribution and the spectral
rigidity by unfolding the spectrum. It is found that increase in number of
energy levels for repulsive BEC induces a transition from a Wigner like form
displaying level repulsion to Poisson distribution for P(s). It does not follow
the GOE prediction. For repulsive interaction, the lower levels are correlated
and manifest level repulsion. For intermediate levels P (s) shows mixed
statistic which clearly signifies the existence of two energy scales: external
trap and interatomic interaction. Whereas for very high levels the trapping
potential dominates, genarating Poisson distribution. Comparison with
mean-field results for lower levels are also presented. For attractive BEC near
the critical point we observe the Shrielman like peak near s=0 which signifies
the presence of large number of quasi-degenerate states.
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