General properties of the spectral form factor in open quantum systems

IF 6.5 2区 物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY
Yi-Neng Zhou, Tian-Gang Zhou, Pengfei Zhang
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引用次数: 0

Abstract

The spectral form factor (SFF) can probe the eigenvalue statistic at different energy scales as its time variable varies. In closed quantum chaotic systems, the SFF exhibits a universal dip-ramp-plateau behavior, which reflects the spectrum rigidity of the Hamiltonian. In this work, we explore the general properties of SFF in open quantum systems. We find that in open systems the SFF first decays exponentially, followed by a linear increase at some intermediate time scale, and finally decreases to a saturated plateau value. We derive general relations between (i) the early-time decay exponent and Lindblad operators; (ii) the long-time plateau value and the number of steady states. We also explain the effective field theory perspective of general behaviors. We verify our theoretical predictions by numerically simulating the Sachdev–Ye–Kitaev (SYK) model, random matrix theory (RMT), and the Bose–Hubbard model.

Abstract Image

开放量子系统频谱形式因子的一般特性
频谱形式因子(SFF)可以随着时间变量的变化探测不同能量尺度的特征值统计量。在封闭的量子混沌系统中,SFF 表现出普遍的浸润-斜坡-高原行为,这反映了哈密顿的谱刚性。在这项工作中,我们探索了开放量子系统中 SFF 的一般特性。我们发现,在开放系统中,SFF 首先呈指数衰减,然后在某个中间时间尺度上呈线性增长,最后下降到饱和高原值。我们推导出 (i) 早期衰变指数与林德布拉德算子之间的一般关系;(ii) 长期高原值与稳态数量之间的一般关系。我们还从有效场论的角度解释了一般行为。我们通过数值模拟 Sachdev-Ye-Kitaev (SYK) 模型、随机矩阵理论 (RMT) 和玻色-哈伯德模型来验证我们的理论预测。
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来源期刊
Frontiers of Physics
Frontiers of Physics PHYSICS, MULTIDISCIPLINARY-
CiteScore
9.20
自引率
9.30%
发文量
898
审稿时长
6-12 weeks
期刊介绍: Frontiers of Physics is an international peer-reviewed journal dedicated to showcasing the latest advancements and significant progress in various research areas within the field of physics. The journal's scope is broad, covering a range of topics that include: Quantum computation and quantum information Atomic, molecular, and optical physics Condensed matter physics, material sciences, and interdisciplinary research Particle, nuclear physics, astrophysics, and cosmology The journal's mission is to highlight frontier achievements, hot topics, and cross-disciplinary points in physics, facilitating communication and idea exchange among physicists both in China and internationally. It serves as a platform for researchers to share their findings and insights, fostering collaboration and innovation across different areas of physics.
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