二次林布兰-克利许兰的线性和非线性响应
Linear and Non-Linear Response of Quadratic Lindbladians
AI总结：
研究开发了用于开放量子系统的林布兰-克利许兰光谱响应形式化方法，用于分析线性和非线性响应特性，并探讨了耗散对光学响应的影响。
AI中文摘要：
二次林布兰-克利许兰涵盖了丰富的耗散电子和玻色量子系统，这些系统已被预测能够容纳新的和奇特的物理现象。在本研究中，我们开发了一种林布兰-克利许兰光谱响应形式化方法，用于开放量子系统，以阐明其稳态响应特性和耗散相变特性，通过有限频率的线性和非线性探测。作为示例，我们利用该形式化方法计算了边界驱动的XY模型在临界点和临界点附近密度和动态自旋易变性、伯恩斯双层石墨烯与耗散导线耦合的线性和非线性光学响应，以及玻色光晶格中的稳态易变性。我们发现XY模型的自旋密度波长在临界指数1/2下发散，动态自旋响应中存在无隙色散模式，这些模式源于底层的自旋密度波序；此外，弱和超强耗散限制的色散模式表现出显著的对应关系，因为边界耗散器在两种情况下都只弱耦合到本体。在伯恩斯双层石墨烯的光学响应中，我们发现磁极化响应随着占据数的增加而减少，这与封闭系统中响应随占据数单调增加不同；我们研究了二次谐波产生和移位电流的影响，并发现这些响应在对称封闭系统中被禁止，但可以通过耗散在这些开放系统中表现出来。我们比较了该形式化方法与其平衡对应物，并绘制了这些非相互作用开放系统与强相互作用封闭系统的类比。
英文摘要：
Quadratic Lindbladians encompass a rich class of dissipative electronic and bosonic quantum systems, which have been predicted to host new and exotic physics. In this study, we develop a Lindblad-Keldysh spectroscopic response formalism for open quantum systems that elucidates their steady-state response properties and dissipative phase transitions via finite-frequency linear and non-linear probes. As illustrative examples, we utilize this formalism to calculate the (1) density and dynamic spin susceptibilities of a boundary driven XY model at and near criticality, (2) linear and non-linear optical responses in Bernal bilayer graphene coupled to dissipative leads, and (3) steady state susceptibilities in a bosonic optical lattice. We find that the XY model spin density wavelength diverges with critical exponent 1/2, and there are gapless dispersive modes in the dynamic spin response that originate from the underlying spin density wave order; additionally the dispersing modes of the weak and ultra-strong dissipation limits exhibit a striking correspondence since the boundary dissipators couple only weakly to the bulk in both cases. In the optical response of the Bernal bilayer, we find that the diamagnetic response can decrease with increasing occupation, as opposed to in closed systems where the response increases monotonically with occupation; we study the effect of second harmonic generation and shift current and find that these responses, forbidden in centrosymmetric closed systems, can manifest in these open systems as a result of dissipation. We compare this formalism to its equilibrium counterpart and draw analogies between these non-interacting open systems and strongly interacting closed systems.
