STATISTICAL PROPERTIES OF EIGENFUNCTIONS OF RANDOM QUASI 1D ONE-PARTICLE HAMILTONIANS
STATISTICAL PROPERTIES OF EIGENFUNCTIONS OF RANDOM QUASI 1D ONE-PARTICLE HAMILTONIANS
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随机拟一维单粒子哈密顿函数本征函数的统计性质
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
A. Mirlin
中科院分区：
文献类型：
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作者：
Y. Fyodorov;A. Mirlin
本文综述了描述量子粒子在有限长L的粗导线中运动的时间反演对称性破缺的随机哈密顿算符的本征函数统计性质的最新分析结果。证明了这一问题等价于研究大型随机带状矩阵在大带宽限制下的性质。这类矩阵与固态物理和量子混沌领域中的许多问题有关。我们找到了下列量分布的解析表达式：i）本征函数振幅|（r）|2在样本的给定点; ii）通过“参与率倒数”测量的本征函数的空间范围P= Δ V dr|（r）|4; iii）数量R=|（r）|2，点r和r′属于样本的相对端。对于一个长样本的数量-（ln R）/L表征的衰减率的本地化的本征函数（李雅普诺夫指数）。与现有的数值结果的关系进行了讨论。
The article reviews recent analytical results concerning statistical properties of eigenfunctions of random Hamiltonians with broken time reversal symmetry describing a motion of a quantum particle in a thick wire of finite length L. It is demonstrated that the problem is equivalent to the study of properties of large Random Banded Matrices in the limit of large width of the band. Matrices of this class are relevant for a number of problems in Solid State physics and in the domain of Quantum Chaos. We find the analytical expressions for the distribution of the following quantities: i) the eigenfunction amplitude |ψ(r)|2 at given point of the sample; ii) spatial extent of the eigenfunction measured by the “inverse participation ratio” P=∫V dr|ψ(r)|4; iii) the quantity R=|ψ(r)ψ(r′)|2, points r and r′ belonging to the opposite ends of the sample. For a long sample the quantity –(ln R)/L characterizes the decay rate of a localized eigenfunction (Lyapunov exponent). Relation with available numerical results is discussed.