NATURE OF ELECTRONIC STATES IN DISORDERED 1-DIMENSIONAL SYSTEMS
NATURE OF ELECTRONIC STATES IN DISORDERED 1-DIMENSIONAL SYSTEMS
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DOI：
10.1098/rspa.1963.0148
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发表时间：
1963-01-01
影响因子：
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通讯作者：
BORLAND, RE
中科院分区：
文献类型：
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作者：
BORLAND, RE
我们考虑一个电子在一个由零电位区域隔开的相同电位的一维无限链的场中运动，这些区域的长度根据概率密度函数(8)分布。如果我们将波动方程实解的约化相定义为arctan （-ψ′/kψ）的主值和єias在第i原子势左侧的点xii处的约化相，则对于所有有界的(s)和足够高的电子能量（theєiare根据概率密度函数分布，该函数取决于从特定齐次边界条件出发的积分方向），都显示出它。这一结果表明，该系统的特征函数是局域化的，即该函数的包络线在某一区域的两侧平均以指数方式衰减。一个随机δ函数链的解析计算明确地给出了节点在高能量下的衰减，并给出了一个液体模型的衰减的数值计算。对1000个随机放置的δ函数链的某些特征函数的计算机计算进一步支持了这一理论。
We consider an electron moving in the field of a one-dimensional infinite chain of identical potentials separated by regions of zero potential, the lengthssof these regions being distributed according to a probability density functionp(8). If we define the reduced phase of a real solution of the wave equation as the principal value of arctan ( —ψ'/kψ) and єias the reduced phase at the pointxiimmediately to the left of theith atomic potential, it is shown for all boundedp(s)and sufficiently high electron energies that theєiare distributed according to a probability density function which depends on the direction of integration from a specified homogeneous boundary condition. This result is shown to imply that the eigenfunctions for such systems are localized in the sense that the envelope of such a function decays on average in an exponential manner on either side of some region. An analytical calculation for a random chain of δ-functions gives the decay of the nodes explicitly for high energies, and numerical calculations of the decay for a liquid model are presented. Further support for the theory is provided by computer calculations of some of the eigenfunctions of a chain of 1000 randomly placed δ-functions.