混沌谱局部林德布拉德系统中的开放系统动力学
Open-system dynamics in local Lindbladians with chaotic spectra
AI总结：
研究满足随机矩阵理论的林德布拉德谱对局部和完全随机动力学的影响，发现早期时间演化准普适，且局域性约束本征算符的尺寸依赖，影响耗散下的算符增长。
AI中文摘要：
我们研究了对于一般林德布拉德算符，其谱满足随机矩阵理论（RMT）时的物理后果，并比较了在一维空间中，空间局部和完全随机林德布拉德动力学的含义。我们发现，谱由RMT描述的林德布拉德算符在密度矩阵非线性量的早期时间演化中表现出准普适性，即对于一般高度纠缠的初始态，早期时间演化与初始态的选择无关。我们数值研究了局域性如何一般性地约束林德布拉德本征算符的尺寸依赖性。这种尺寸依赖性意味着，在热力学极限下，线性可观测量（如局部算符的期望值）对谱体外的本征模高度敏感，并在限制耗散存在下的算符增长中起核心作用。我们发现，当单点耗散占主导时，即使存在两点跳变算符，算符的退相干大致与其泡利权重成线性关系。然而，当仅两点耗散占主导时，对于数值可访问的系统尺寸，这种算符尺寸的一般趋势可能被违反，导致长寿命的高泡利权重算符。
英文摘要：
We investigate the physical consequences of having a spectrum that satisfies random matrix theory (RMT) for generic Lindbladians, and compare its implications for spatially local and completely random Lindblad dynamics in one spatial dimension. We find that Lindbladians whose spectrum is described by RMT exhibit quasiuniversal early-time dynamics for quantities nonlinear in the density matrix, in the sense that for generic, highly entangled initial states, the early time evolution is independent of the choice of initial state. We numerically investigate how locality generically imposes constraints on the size-dependence of Lindblad eigenoperators. This size dependence implies that linear observables, such as expectation values of local operators, are highly sensitive to eigenmodes outside the bulk of the spectrum in the thermodynamic limit, and plays a central role in limiting operator growth in the presence of dissipation. We find that when single-site dissipation dominates, an operator's decoherence scales approximately linearly with its Pauli weight, even in the presence of two-site jump operators. When two-site only dissipation dominates, however, this generic trend in operator size can be violated for numerically accessible system sizes, leading to long-lived high Pauli-weight operators.
