Saturation of number variance in embedded random-matrix ensembles.
We study fluctuation properties of embedded random matrix ensembles of noninteracting particles. For ensemble of two noninteracting particle systems, we find that unlike the spectra of classical random matrices, correlation functions are nonstationary. In the locally stationary region of spectra, we study the number variance and the spacing distributions. The spacing distributions follow the Poisson statistics, which is a key behavior of uncorrelated spectra. The number variance varies linearly as in the Poisson case for short correlation lengths but a kind of regularization occurs for large correlation lengths, and the number variance approaches saturation values. These results are known in the study of integrable systems but are being demonstrated for the first time in random matrix theory. We conjecture that the interacting particle cases, which exhibit the characteristics of classical random matrices for short correlation lengths, will also show saturation effects for large correlation lengths.
School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India.
Ravi
R
Prakash
School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India.
Akhilesh
A
Pandey