Roy Kamalika, Chakrabarti Barnali, Biswas Anindya, Kota V K B, Haldar Sudip Kumar
Department of Physics, Lady Brabourne College, P1/2 Suhrawardi Avenue, Kolkata 700017, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jun;85(6 Pt 1):061119. doi: 10.1103/PhysRevE.85.061119. Epub 2012 Jun 20.
It has been recently shown numerically that the transition from integrability to chaos in quantum systems and the corresponding spectral fluctuations are characterized by 1/f^{α} noise with 1≤α≤2. The system of interacting trapped bosons is inhomogeneous and complex. The presence of an external harmonic trap makes it more interesting as, in the atomic trap, the bosons occupy partly degenerate single-particle states. Earlier theoretical and experimental results show that at zero temperature the low-lying levels are of a collective nature and high-lying excitations are of a single-particle nature. We observe that for few bosons, the P(s) distribution shows the Shnirelman peak, which exhibits a large number of quasidegenerate states. For a large number of bosons the low-lying levels are strongly affected by the interatomic interaction, and the corresponding level fluctuation shows a transition to a Wigner distribution with an increase in particle number. It does not follow Gaussian orthogonal ensemble random matrix predictions. For high-lying levels we observe the uncorrelated Poisson distribution. Thus it may be a very realistic system to prove that 1/f^{α} noise is ubiquitous in nature.
最近的数值研究表明，量子系统中从可积性到混沌的转变以及相应的谱涨落具有1/f^α噪声的特征，其中1≤α≤2。相互作用的捕获玻色子系统是不均匀且复杂的。外部谐波陷阱的存在使其更具趣味性，因为在原子陷阱中，玻色子占据部分简并的单粒子态。早期的理论和实验结果表明，在零温度下，低能级具有集体性质，高能级激发具有单粒子性质。我们观察到，对于少量玻色子，P(s)分布显示出什尼尔曼峰，该峰表现出大量的准简并态。对于大量玻色子，低能级受到原子间相互作用的强烈影响，相应的能级涨落在粒子数增加时显示出向维格纳分布的转变。它并不遵循高斯正交系综随机矩阵的预测。对于高能级，我们观察到不相关的泊松分布。因此，它可能是一个非常现实的系统，用以证明1/f^α噪声在自然界中无处不在。
