准一维系统中Lyapunov指数的性质

The property of Lyapunov exponents in aquasi-one-dimensional system

建立了Anderson模型的传输矩阵,并采用传输矩阵法求解了准一维系统中的Lyapuov指数(LE),LE与电子局域化长度成反比,LE很好地描述了电子的局域化性质.通过计算SPS理论中的τ值,研究了在一维系统中成立的标度方程是否适用于准一维系统.本文还给出了多条链中不同通道的LE之间关联的计算方法,计算了2个通道和3个通道之间关联随着系统无序度的变化情况.

Lyapunov exponents in a quasi-one-dimensional system were calculated by transfer matrix.Since Lyapunov exponents are inversely proportional to localization length,the property of electron can be obtained.The problem that whether the scaling equation in SPS theory can be generalized to quasi-one-dimensional system is solved by calculatingτ.Correlation of different exponents was calculated and variance of correlation with increased disorder strength was obtained.When correlation of 2 and 3 Lyapunov exponents in Anderson model is acertained,with disorder in a certain range,the correlation is almost equal to zero.