Random matrix ensembles with column/row constraints: II

Abstract

We numerically analyze the random matrix ensembles of real-symmetric matrices with column/row constraints for many system conditions e.g. disorder type, matrix-size and basisconnectivity. The results reveal a rich behavior hidden beneath the spectral statistics and also confirm our analytical predictions, presented in part I of this paper, about the analogy of their spectral fluctuations with those of a critical Brownian ensemble which appears between Poisson and Gaussian orthogonal ensemble.

Random matrix ensembles with column/row constraints: I

“…The statistical behavior of the ensemble is therefore expected to lie between Poisson and GOE, with bulk behavior more close to GOE than that of the edge. This behavior is confirmed by our numerics discussed in [48].…”

“…(29), the 1 st term in the above can be rewritten as zf mn . The 2 nd term, a sum the results, which it leads to, are supported by our numerical analysis discussed in [48]). Substitution of eq.…”

“…Furthermore as the level-repulsion between all non-zero eigenvalue pairs is same for both CCGE and BE, the local correlations in the (N − 1) dimensional eigenvalue space (excluding zero eigenvalue) of a N × N CCGE are expected to be analogous to that of a (N − 1) × (N − 1) BE. The analogy is confirmed by the numerics given in [48].…”

“…Thus the ensemble averaged level density of the CCE is expected to deviate from that of the BE near zero energy; (this is also confirmed by the numerics shown in figure 12(a) of [48]).…”

“…with N z = N −z −1. For the case b 0 = b 1 = 0 (considered in [48] for our numerical analysis), this gives a typical diagonal almost z times of a typical off-diagonal ( therefore weaker than the case II, see eq. (27)).…”