非平衡稳态的利nderbladian反向工程：一种可扩展的空域方法
Lindbladian reverse engineering for general non-equilibrium steady states: A scalable null-space approach
AI总结：
本文提出了一种可扩展的空域方法，用于非平衡稳态的利nderbladian反向工程，通过线性问题解决重建主方程的挑战。
AI中文摘要：
开放系统动力学的研究在基础方面和量子技术的潜在应用方面都具有重要性。在更简单且最常研究的情况下，系统的动力学可以由利nderblad主方程描述。然而，识别导致一般非平衡稳态（NESS）的利nderbladian通常是非平凡且具有挑战性的。在此，我们介绍了一种方法，用于根据任何目标NESS重建相应的利nderblad主方程，即利nderbladian反向工程（LRE）方法。该方法将重建任务映射到一个简单的线性问题。具体来说，将对角化一个相关矩阵，其元素是NESS可观测值，其大小与哈密顿量（利nderblad跃迁算符）假设中的项数成线性（最多二次）关系。相关矩阵的核（空域）对应于利nderbladian解。此外，该映射定义了LRE的iff条件，它在所提出的设置中确定了此类演化的可行性。我们通过不同系统展示了该方法，从玻色子高斯系统、耗散驱动的集体自旋和随机局部自旋模型。
英文摘要：
The study of open system dynamics is of paramount importance both from its fundamental aspects as well as from its potential applications in quantum technologies. In the simpler and most commonly studied case, the dynamics of the system can be described by a Lindblad master equation. However, identifying the Lindbladian that leads to general non-equilibrium steady states (NESS) is usually a non-trivial and challenging task. Here we introduce a method for reconstructing the corresponding Lindbaldian master equation given any target NESS, i.e., a \textit{Lindbladian Reverse Engineering} ($\mathcal{L}$RE) approach. The method maps the reconstruction task to a simple linear problem. Specifically, to the diagonalization of a correlation matrix whose elements are NESS observables and whose size scales linearly (at most quadratically) with the number of terms in the Hamiltonian (Lindblad jump operator) ansatz. The kernel (null-space) of the correlation matrix corresponds to Lindbladian solutions. Moreover, the map defines an iff condition for $\mathcal{L}$RE, which works as both a necessary and a sufficient condition; thus, it not only defines, if possible, Lindbladian evolutions leading to the target NESS, but also determines the feasibility of such evolutions in a proposed setup. We illustrate the method in different systems, ranging from bosonic Gaussian systems, dissipative-driven collective spins and random local spin models.
