论文标题
精确的dirac-bogoliubov-de基因动力学，用于不均匀量子液体
Exact Dirac-Bogoliubov-de Gennes Dynamics for Inhomogeneous Quantum Liquids
论文作者
论文摘要
我们研究了由Tomonaga-luttinger-liquid理论描述的不均匀1+1维量子多体系统，其一般传播速度和Luttinger参数在太空中平稳变化，相当于自由玻色子共同现场理论的不均匀紧缩半径。在低能描述中，该模型显着出现，包括针对捕获的超低原子，而在这里我们提出了一种具有不均匀相互作用的量子大厅边缘的应用。该动力学显示由一对耦合的连续性方程与局部间隙相同，并通过分析方式求解。我们使用Magnus膨胀获得了它们的确切绿色功能和散射矩阵，该矩阵概括了与铅相结合的共形界面和量子线的先前结果。我们的结果明确描述了量子淬火后的晚期演化，包括不均匀的相互作用淬灭，以及耦合量子霍尔边缘之间的Andreeve反射，揭示了对平稳性或近期的细节的普遍依赖。
We study inhomogeneous 1+1-dimensional quantum many-body systems described by Tomonaga-Luttinger-liquid theory with general propagation velocity and Luttinger parameter varying smoothly in space, equivalent to an inhomogeneous compactification radius for free boson conformal field theory. This model appears prominently in low-energy descriptions, including for trapped ultracold atoms, while here we present an application to quantum Hall edges with inhomogeneous interactions. The dynamics is shown to be governed by a pair of coupled continuity equations identical to inhomogeneous Dirac-Bogoliubov-de Gennes equations with a local gap and solved by analytical means. We obtain their exact Green's functions and scattering matrix using a Magnus expansion, which generalize previous results for conformal interfaces and quantum wires coupled to leads. Our results explicitly describe the late-time evolution following quantum quenches, including inhomogeneous interaction quenches, and Andreev reflections between coupled quantum Hall edges, revealing a remarkably universal dependence on details at stationarity or at late times out of equilibrium.
