Localization of the electronic states in a nonstationary chaotic field with long-range correlation

The localization problem in nonstationary chaotic field with a long-range correlation, which is generated by the modified Bernoulli map, is numerically studied. The map can generate a stationary (B<2) and nonstationary (Bgreater than or equal to2) sequence by changing the parameter B. We investigate the effect of correlation on localization in the electronic states by the Lyapunov exponent gamma (the inverse localization length) and the localization length xi in the nonstationary regime. At the band center the potential strength, W, dependence of the Lyapunov exponent shows gammasimilar toW(2) independent of the correlation strength B, while at the band edge the scaling form changes from gammasimilar toW(2/3) to gammasimilar toW(1/2) as the correlation increases. It is also numerically shown that the B dependence of the Lyapunov exponent obeys gammaproportional to-B for Bless than or equal to2 and exponentially decreases for B>2. Furthermore we investigate the system size, N, dependence of the localization length. It is confirmed that in the strongly correlated cases (Bless than or equal to3.0) the exponential localization remains, i.e., gammasimilar toN(nu)(nusimilar to0), even for the weak potential strength (W=0.01) in the thermodynamic limit.