The Laplacian on a random one-dimensional lattice
The Laplacian on a random one-dimensional lattice
复制标题
随机一维晶格上的拉普拉斯算子
DOI：
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发表时间：
1984
期刊：
影响因子：
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通讯作者：
B. Derrida
中科院分区：
文献类型：
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作者：
E. Gardner;C. Itzykson;B. Derrida
作者研究了随机一维晶格上（负）拉普拉斯算子的谱。它在整个正实轴上单调延伸，对于小值具有连续极限行为。作者在整个范围内发现了预期的本地化效果。他们使用了多种技术，这些技术被证明与蒙特卡罗模拟一致且一致。它们包括小无序展开式和大无序展开式、概率分布的直接积分方程以及复制方法。后者也用于研究格林函数。
The authors study the spectrum of (minus) the Laplacian on a random one-dimensional lattice. It extends monotonically throughout the positive real axis with a continuum limit behaviour for small values. The authors find as expected localisation effects throughout the whole range. They use a variety of techniques which are shown to be consistent and in agreement with a Monte Carlo simulation. They include small and large disorder expansions, direct integral equations for probability distributions as well as the replica method. The latter is also used to investigate Green functions.