一般开放量子系统的耗散与退相干
Dissipation and decoherence for generic open quantum systems
摘要：
本文研究了一般的具有马尔可夫耗散的开放量子系统，重点研究了一类Lindblad形式的随机Liouvillian算子，该算子具有独立的随机耗散通道（跳跃算子）和一个随机哈密顿量.我们进行了彻底的数值研究，重点是全球的光谱特征，光谱间隙，稳态纯度和统计。我们建立，所有的属性遵循三个不同的制度作为耗散强度的函数，其边界取决于特定的观察。在每一个政权，我们确定的标度指数与耗散强度和系统的大小。在分析方面，我们计算在任意耗散的平均谱间隙，并提供简单的封闭形式的表达式，在强和弱耗散强度的渐近值。我们还考虑在一般复杂的光谱，如Liouvillian的光谱相关性。我们介绍和研究，分析和数值计算，复杂的最近邻间距的下一个最近邻间距的比例。除了通常的水平排斥，我们发现复杂的间距比有一个非平凡的角度依赖性，这提供了一个独特的签名的量子混沌。它区分了支持泊松统计的平比分布特征的可积系统和符合随机矩阵理论统计的混沌耗散量子系统。我们将这种新的量子混沌签名应用于随机Liouvillians和边界驱动的耗散自旋链。本论文的结果可以帮助理解一般耗散系统的长时间动力学、定态性质和谱关联。
英文摘要：
We study generic open quantum systems with Markovian dissipation, focusing on a class of stochastic Liouvillian operators of Lindblad form with independent random dissipation channels (jump operators) and a random Hamiltonian. We perform a thorough numerical study, focusing on global spectral features, the spectral gap, and the steady-state purity and statistics. We establish that all properties follow three different regimes as a function of the dissipation strength, whose boundaries depend on the particular observable. Within each regime, we determine the scaling exponents with the dissipation strength and system size. On the analytical side, we compute the average spectral gap at arbitrary dissipation and provide simple closed-form expressions for the asymptotic values at strong and weak dissipation strength. We also consider spectral correlations in generic complex spectra, such as that of the Liouvillian. We introduce and study, both analytically and numerically, the complex ratio of the nearest-neighbor spacing by next-to-nearest-neighbor spacing. Besides the usual level repulsion, we find that complex spacing ratios have a nontrivial angular dependence which offers a distinct signature of quantum chaos. It distinguishes integrable systems, which support the flat ratio distribution characteristic of Poisson statistics, and chaotic dissipative quantum systems, which conform to Random Matrix Theory statistics. We apply this new signature of quantum chaos to random Liouvillians and boundary-driven dissipative spin-chains. The results of this thesis can help understand the long-time dynamics, steady-state properties, and spectral correlations of generic dissipative systems.
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