Stöckmann H-J, Kohler H
Fachbereich Physik der Philipps-Universität Marburg, Renthof 5, D-35032 Marburg, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Jun;73(6 Pt 2):066212. doi: 10.1103/PhysRevE.73.066212. Epub 2006 Jun 8.
The concept of fidelity has been introduced to characterize the stability of a quantum-mechanical system against perturbations. The fidelity amplitude is defined as the overlap integral of a wave packet with itself after the development forth and back under the influence of two slightly different Hamiltonians. It was shown by Prosen and Znidaric in the linear-response approximation that the decay of the fidelity is frozen if the Hamiltonian of the perturbation contains off-diagonal elements only. In the present work the results of Prosen and Znidaric are extended by a supersymmetry calculation to arbitrary strengths of the perturbation for the case of an unperturbed Hamiltonian taken from the Gaussian orthogonal ensemble and a purely imaginary antisymmetric perturbation. It is found that for the exact calculation the freeze of fidelity is only slightly reduced as compared to the linear-response approximation. This may have important consequences for the design of quantum computers.
保真度的概念已被引入，用于表征量子力学系统抵抗微扰的稳定性。保真度振幅被定义为一个波包在两个略有不同的哈密顿量影响下向前和向后演化后自身的重叠积分。普罗森（Prosen）和兹尼达里克（Znidaric）在线性响应近似中表明，如果微扰的哈密顿量仅包含非对角元，则保真度的衰减会被冻结。在本工作中，对于取自高斯正交系综的未微扰哈密顿量和纯虚反对称微扰的情况，通过超对称计算将普罗森和兹尼达里克的结果扩展到任意强度的微扰。结果发现，与线性响应近似相比，精确计算时保真度的冻结仅略有降低。这可能对量子计算机的设计产生重要影响。
