Localization of the electronic states in non-stationary chaotic field with long-range correlation: off-diagonal model

The localization problem in stationary and non-stationary chaotic field with long-range correlation, which is generated by modified Bernoulli map, is numerically studied. The map can generate stationary (B < 2) and non-stationary (B greater than or equal to 2) sequence by changing the parameter B. We investigate effect of the correlation on the localization in the electronic states of the off-diagonal model by Lyapunov exponent gamma (inverse localization length) and localization length xi in the stationary and nonstationary regime. At the band center (E = 0) the localization length diverges as xi similar to \E\(-2) independently of B. It is also numerically shown that the B-dependence of the Lyapunov exponent obeys, gamma alpha -B for B less than or equal to 2, and exponentially decreases for B > 2. Furthermore, we investigate the system size N-dependence of the localization length. It is confirmed that even in the strongly correlated cases (B less than or equal to 3.0) the exponential localization is remained, i.e., xi similar to N-nu(nu similar to 0), in the thermodynamic limit, except for the band center energy. (C) 2004 Elsevier B.V. All rights reserved.