Universal correlations for deterministic plus random Hamiltonians.
Universal correlations for deterministic plus random Hamiltonians.
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确定性加随机哈密顿量的通用相关性。
DOI：
10.1103/physreve.51.5442
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发表时间：
1994
期刊：
影响因子：
--
通讯作者：
Zee
中科院分区：
文献类型：
--
作者：
Brézin;Hikami;Zee
We consider the (smoothed) average correlation between the density of energy levels of a disordered system, in which the Hamiltonian is equal to the sum of a deterministic ${\mathit{H}}_{0}$, and of a random potential cphi. Remarkably, this correlation function may be explicitly determined in the limit of large matrices, for any unperturbed ${\mathit{H}}_{0}$ and for a class of probability distribution P(cphi) of the random potential. We find a compact representation of the correlation function. From this representation one readily obtains the short distance behavior, which has been conjectured in various contexts to be universal. Indeed we find that it is totally independent of both ${\mathit{H}}_{0}$ and P(cphi).
We consider the (smoothed) average correlation between the density of energy levels of a disordered system, in which the Hamiltonian is equal to the sum of a deterministic ${\mathit{H}}_{0}$, and of a random potential cphi. Remarkably, this correlation function may be explicitly determined in the limit of large matrices, for any unperturbed ${\mathit{H}}_{0}$ and for a class of probability distribution P(cphi) of the random potential. We find a compact representation of the correlation function. From this representation one readily obtains the short distance behavior, which has been conjectured in various contexts to be universal. Indeed we find that it is totally independent of both ${\mathit{H}}_{0}$ and P(cphi).