Herrera-González I F, Izrailev F M, Makarov N M
Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla, Puebla 72570, México.
Instituto de Ciencias, Benemérita Universidad Autónoma de Puebla, Priv. 17 Norte No. 3417, Col. San Miguel Hueyotlipan, Puebla, Puebla 72050, México.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Nov;88(5):052108. doi: 10.1103/PhysRevE.88.052108. Epub 2013 Nov 7.
We study localization properties of the eigenstates and wave transport in a one-dimensional system consisting of a set of barriers and/or wells of fixed thickness and random heights. The inherent peculiarity of the system resulting in the enhanced Anderson localization is the presence of the resonances emerging due to the coherent interaction of the waves reflected from the interfaces between the wells and/or barriers. Our theoretical approach allows to derive the localization length in infinite samples both out of the resonances and close to them. We examine how the transport properties of finite samples can be described in terms of this length. It is shown that the analytical expressions obtained by standard methods for continuous random potentials can be used in our discrete model, in spite of the presence of resonances that cannot be described by conventional theories. All our results are illustrated with numerical data manifesting an excellent agreement with the theory.
我们研究了由一组具有固定厚度和随机高度的势垒和/或势阱组成的一维系统中本征态的局域化性质和波传输。该系统导致增强的安德森局域化的固有特性是由于从势阱和/或势垒之间的界面反射的波的相干相互作用而出现的共振。我们的理论方法能够得出无限样本在远离共振和接近共振时的局域化长度。我们研究了如何用这个长度来描述有限样本的传输性质。结果表明，尽管存在传统理论无法描述的共振，但通过标准方法得到的连续随机势的解析表达式仍可用于我们的离散模型。我们所有的结果都用数值数据进行了说明，这些数据与理论表现出了极好的一致性。
