量子关联函数从短实时动力学的最大熵扩展
Maximum-Entropy Extension of Quantum Correlation Functions from Short Real-Time Dynamics
- Phasecraft Ltd.（Phasecraft有限公司）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出基于Burg最大熵原理的量子关联函数时间序列扩展方法，通过Yule-Walker方程求解全极点自回归模型，实现从短时数据重建谱密度，保证谱正性并适用于矩阵情形。
AI中文摘要：
关联函数对于理解量子系统的行为至关重要，其谱直接提供了准粒子和集体激发的信息。然而，要达到足够谱分辨率所需的长时间演化，对经典和量子模拟而言都极具挑战。在本工作中，我们提出了一种基于量子关联函数与平稳随机过程协方差序列之间联系的原则性方法，用于扩展量子关联函数的时间序列并重建其谱密度。这一联系使我们能够应用Burg最大熵原理，找到与关联函数测量值相容的最不预设的扩展，该扩展对应于一个全极点自回归模型，其系数通过求解一组Yule-Walker方程获得。所得扩展在构造上即为半正定的，从而保证了谱的正性以及总谱权重求和规则的自动满足。该方法适用于标量和矩阵值关联函数，包括具有高度结构化或连续谱的关联函数。向矩阵情形的推广使得可以用模拟时间换取额外的关联函数测量，从而即使在存在噪声的情况下，也能从短时数据实现准确的时间序列扩展和谱重建。
英文摘要：
Correlation functions are central to understanding the behavior of quantum systems, with their spectra giving direct access to quasiparticle and collective excitations. However, the long-time evolution required for sufficient spectral resolution is challenging to reach for both classical and quantum simulations. In this work, we introduce a principled approach for extending time series of quantum correlation functions and reconstructing their spectral densities, based on their connection with covariance sequences of stationary stochastic processes. This connection enables us to apply Burg's maximum-entropy principle to find the least-committal extension compatible with the measured values of the correlation function, which corresponds to an all-pole autoregressive model whose coefficients solve a set of Yule--Walker equations. The resulting extension is positive semi-definite by construction, guaranteeing the positivity of the spectrum and the automatic satisfaction of its total spectral weight sum rule. The approach applies to both scalar and matrix-valued correlation functions, including those with highly structured or continuous spectra. The generalization to the matrix case makes it possible to trade simulation time for additional measured correlation functions, enabling accurate time-series extension and spectral reconstruction from short-time data, even in the presence of noise.
