A random matrix formulation of fidelity decay
A random matrix formulation of fidelity decay
复制标题
保真度衰减的随机矩阵公式
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
T. Seligman
中科院分区：
文献类型：
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作者：
T. Gorin;T. Prosen;T. Seligman
我们建议在随机矩阵框架中研究回波动力学，在这里我们假设扰动是与时间无关的，随机的和正交不变的。这使得我们可以使用一个基础，其中未扰动的哈密顿量是对角的，因此它的性质在很大程度上取决于它的谱统计。我们专注于通常与混沌和忽视长期的谱密度变化的谱相关性的影响。我们得到的线性响应制度的保真度衰减的分析结果。为了扩展有效域，我们对线性响应结果进行指数化。所得的表达式在微扰极限下是精确的，是“费米黄金法则”和微扰区域之间过渡区域的精确近似，正如确定性混沌系统的例子所验证的那样。为了感知光谱刚度的影响，我们也将我们的模型应用于随机光谱和等距光谱的极端情况。在我们的分析近似，以及在广泛的蒙特卡罗计算，我们发现，保真度衰减是最快的随机光谱和最慢的等距的，而经典的合奏之间。我们得出结论，光谱刚度系统地提高保真度。
We propose to study echo dynamics in a random-matrix framework, where we assume that the perturbation is time-independent, random and orthogonally invariant. This allows us to use a basis in which the unperturbed Hamiltonian is diagonal and its properties are thus largely determined by its spectral statistics. We concentrate on the effect of spectral correlations usually associated with chaos and disregard secular variations in spectral density. We obtain analytical results for the fidelity decay in the linear-response regime. To extend the domain of validity, we heuristically exponentiate the linear-response result. The resulting expressions, exact in the perturbative limit, are accurate approximations in the transition region between the ‘Fermi golden rule’ and the perturbative regimes, as verified by example for a deterministic chaotic system. To sense the effect of spectral stiffness, we apply our model also to the extreme cases of random spectra and equidistant spectra. In our analytical approximations as well as in extensive Monte Carlo calculations, we find that fidelity decay is fastest for random spectra and slowest for equidistant ones, while the classical ensembles lie in between. We conclude that spectral stiffness systematically enhances fidelity.