Random Analytic Chaotic Eigenstates
Random Analytic Chaotic Eigenstates
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随机解析混沌本征态
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
P. Leboeuf
中科院分区：
文献类型：
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作者：
P. Leboeuf
研究了随机解析函数ψ(Z)作为全混沌系统本征函数的相空间模型的统计性质。我们把以前证明的球面相空间[SU(2)多项式]的ψ(Z)的零点等分布定理推广到平面和双曲平面上。对于具有时间反转对称性的系统，计算了三个几何形状的实根的个数。在半经典状态下，局域关联函数是普适的，与所考虑的系统或相空间的几何无关。特别地，ψ的自相关函数由高斯函数给出。讨论了该模型与高斯随机函数假设和随机矩阵理论之间的联系。
The statistical properties of random analytic functions ψ(z) are investigated as a phase-space model for eigenfunctions of fully chaotic systems. We generalize to the plane and to the hyperbolic plane a theorem concerning the equidistribution of the zeros of ψ(z) previously demonstrated for a spherical phase space [SU(2) polynomials]. For systems with time-reversal symmetry, the number of real roots is computed for the three geometries. In the semiclassical regime, the local correlation functions are shown to be universal, independent of the system considered or the geometry of phase space. In particular, the autocorrelation function of ψ is given by a Gaussian function. The connections between this model and the Gaussian random function hypothesis as well as the random matrix theory are discussed.