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 establish that the global spectral features, the spectral gap, and the steady-state properties follow three different regimes as a function of the dissipation strength, whose boundaries depend on the particular quantity. Within each regime, we determine the scaling exponents with the dissipation strength and system size. We find that, for two or more dissipation channels, the spectral gap increases with the system size. The spectral distribution of the steady state is Poissonian at low dissipation strength and conforms to that of a random matrix once the dissipation is sufficiently strong. Our results can help to understand the long-time dynamics and steady-state properties of generic dissipative systems.

中文翻译：

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随机Liouvillians的光谱和稳态性质

我们研究具有马尔可夫耗散的通用开放量子系统，重点研究一类具有独立随机耗散通道（跳跃算子）和随机哈密顿量的Lindblad形式的随机Liouvillian算子。我们确定全局光谱特征，光谱间隙和稳态特性遵循三种不同的机制作为耗散强度的函数，耗散强度的边界取决于特定的数量。在每个方案中，我们根据耗散强度和系统大小确定缩放指数。我们发现，对于两个或更多的耗散通道，频谱间隙随系统大小而增加。稳态光谱分布在低耗散强度下为泊松分布，一旦耗散足够强，则符合随机矩阵的分布。