动量依赖的量子Ruelle-Pollicott共振在平移不变多体系统中的应用
Momentum dependent quantum Ruelle-Pollicott resonances in translationally invariant many-body systems
AI总结：
本文研究平移不变量子多体系统中动量依赖的Ruelle-Pollicott共振，通过算子传播子谱揭示关联函数衰减速率差异，预测随机矩阵环大小，并发现混合区域中幂律衰减及几乎守恒算子导致的时间尺度差异。
摘要：
我们通过无限系统中动量分辨的算子传播子谱来研究平移不变的量子多体晶格系统中的Ruelle-Pollicott共振。动量依赖性揭示了对关联函数衰减的洞察，表明根据其对称性，不同的关联函数通常以不同的速率衰减。聚焦于 kicked Ising 模型，谱通常由一个环形随机矩阵般的环组成，其大小我们进行了理论预测，以及少数孤立的共振。我们识别了几个有趣的区域，包括一个具有幂律衰减关联函数的混合区域。在该区域中，我们还观察到由于一个几乎守恒的算子，不同关联函数的时间尺度存在巨大差异。我们推测了算子传播子奇异值的精确表达式，表明它在某个特殊点变得奇异。
英文摘要：
We study Ruelle-Pollicott resonances in translationally invariant quantum many-body lattice systems via spectra of a momentum-resolved operator propagator on infinite systems. Momentum dependence gives insight into the decay of correlation functions, showing that, depending on their symmetries, different correlation functions in general decay with different rates. Focusing on the kicked Ising model the spectrum seems to be typically composed of an annular random matrix like ring whose size we theoretically predict, and few isolated resonances. We identify several interesting regimes, including a mixing regime with a power-law decay of correlation functions. In that regime we also observe a huge difference in time-scales of different correlation functions due to an almost conserved operator. An exact expression for the singular values of the operator propagator is conjectured, showing that it becomes singular at a special point.
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