Distribution of matrix elements of chaotic systems.
Distribution of matrix elements of chaotic systems.
复制标题
混沌系统矩阵元素的分布。
DOI：
10.1103/physreva.34.591
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发表时间：
1986
期刊：
影响因子：
--
通讯作者：
Asher Peres
中科院分区：
文献类型：
--
作者：
Mario Feingold;Asher Peres
当一个量子系统有一个混沌的经典模拟时，它的能量表示中的矩阵元素与经典系统的各种微正则平均密切相关。对角矩阵元素聚集在经典期望值周围，具有与非对角矩阵元素的值类似的波动。后者又与经典的自相关性有关。这些结果意味着量子微扰理论在半经典极限progation → 0时一定会失效：两个任意接近的哈密顿量通常具有完全不同的本征向量集。
When a quantum system has a chaotic classical analog, its matrix elements in the energy representation are closely related to various microcanonical averages of the classical system. The diagonal matrix elements cluster around the classical expectation values, with fluctuations similar to the values of the off-diagonal matrix elements. The latter in turn are related to the classical autocorrelations. These results imply that quantum perturbation theory must fail, for chaotic systems, in the semiclassical limit ħ→ 0: Two arbitrarily close Hamiltonians have, in general, completely different sets of eigenvectors.