自平均谱形状因子中的幺正性破缺
Unitarity breaking in self-averaging spectral form factors
AI总结：
本文证明谱形状因子的滤波器、无序和时间平均对应混合幺正量子信道中的幺正性破缺，并证明频率和能量滤波器可使其在长时间下自平均。
摘要：
量子系统能谱两点关联函数的复傅里叶变换被称为谱形状因子（SFF）。它构成了物相和量子混沌的重要诊断工具。在黑洞物理学中，它描述了热场双态在幺正时间演化下的生存概率（保真度）。然而，具有一般谱的孤立量子系统的谱形状因子的详细性质会被大的时间涨落抹平，其最小化需要无序或时间平均。这一要求对任意系统尺寸都成立，即谱形状因子是非自平均的。利用该量的基于保真度的解释，我们证明使用滤波器、无序和时间平均的谱形状因子涉及幺正性破缺，即由抑制量子噪声的量子信道描述的开放量子动力学。具体而言，对哈密顿量系综的平均、时间平均和频率滤波器可以由混合幺正量子信道类描述，其中信息损失可以被恢复。频率滤波器与推广能量退相的时间连续主方程相关联。我们还讨论了本征值滤波器的使用。它们与无量子跳跃的非厄米哈密顿量演化相联系，其长时间行为由哈密顿量形变描述。我们证明频率和能量滤波器使谱形状因子在长时间下自平均。
英文摘要：
The complex Fourier transform of the two-point correlator of the energy spectrum of a quantum system is known as the spectral form factor (SFF). It constitutes an essential diagnostic tool for phases of matter and quantum chaos. In black hole physics, it describes the survival probability (fidelity) of a thermofield double state under unitary time evolution. However, detailed properties of the SFF of isolated quantum systems with generic spectra are smeared out by large temporal fluctuations, whose minimization requires disorder or time averages. This requirement holds for any system size, that is, the SFF is non-self averaging. Exploiting the fidelity-based interpretation of this quantity, we prove that using filters, disorder and time averages of the SFF involve unitarity breaking, i.e., open quantum dynamics described by a quantum channel that suppresses quantum noise. Specifically, averaging over Hamiltonian ensembles, time averaging, and frequency filters can be described by the class of mixed-unitary quantum channels in which information loss can be recovered. Frequency filters are associated with a time-continuous master equation generalizing energy dephasing. We also discuss the use of eigenvalue filters. They are linked to non-Hermitian Hamiltonian evolution without quantum jumps, whose long-time behavior is described by a Hamiltonian deformation. We show that frequency and energy filters make the SFF self-averaging at long times.
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