Recovery of the fidelity amplitude for the Gaussian ensembles
Recovery of the fidelity amplitude for the Gaussian ensembles
复制标题
高斯系综保真度幅度的恢复
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
R. Schaefer
中科院分区：
文献类型：
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作者：
H. Stoeckmann;R. Schaefer
使用超对称技术获得了保真度振幅fφ (τ) =⟨ψ(0)|exp(2πiHϵτ) exp(−2πiH0τ)|ψ(0)⟩的平均值的解析表达式，其中，H0和hφ分别取自高斯酉系综（GUE）或高斯正交系综（GOE）。根据文献的结果，只要扰动强度与平均水平间距相比较小，就会观察到保真度振幅的高斯衰减，而对于更强的扰动，则会发生单指数衰减的变化。然而，在接近海森堡时间τ = 1时，发现了保真度的部分恢复，这是迄今为止未被注意到的。对三种高斯系综进行了随机矩阵模拟。对于GOE和GUE的情况，它们与分析结果完全一致。
Using supersymmetry techniques analytical expressions for the average of the fidelity amplitude fϵ(τ) = ⟨ψ(0)|exp(2πiHϵτ) exp(−2πiH0τ)|ψ(0)⟩ are obtained, where , and H0 and Hϵ are taken from the Gaussian unitary ensemble (GUE) or the Gaussian orthogonal ensemble (GOE), respectively. As long as the perturbation strength is small compared to the mean level spacing, a Gaussian decay of the fidelity amplitude is observed, whereas for stronger perturbations a change to a single-exponential decay takes place, in accordance with results from the literature. Close to the Heisenberg time τ = 1, however, a partial revival of the fidelity is found, which hitherto remained unnoticed. Random matrix simulations have been performed for the three Gaussian ensembles. For the case of the GOE and the GUE they are in perfect agreement with the analytical results.