论文标题
耗散晶格中的工程假想的史塔克梯子：被动$ \ Mathcal {pt} $对称，k对称和局部阻尼
Engineering imaginary stark ladder in a dissipative lattice: passive $\mathcal{PT}$ symmetry, K symmetry and localized damping
论文作者
论文摘要
我们研究了一个假想的史塔克梯子模型，并提出了在耗散链中实现该模型，线性依赖于站点依赖性的耗散强度。由于存在$ k $ -smmetry和被动$ \ Mathcal {pt} $对称性，该型号的功能与其Hermitian的功能截然不同。随着耗散强度的提高，该系统首先经历一个被动的$ \ MATHCAL {PT} $ - 对称破坏过渡，随着转移的特征值从真实变为复杂，然后是$ K $ - $ - $ - $ - 符号的恢复过渡，其特征是纯粹的假想光谱的出现与纯粹的间隔相等。因此，特征态从$ \ MATHCAL {pt} $ - 不间断的扩展状态转变为$ \ Mathcal {pt} $ - 损坏状态，最后是史塔克本地化状态。在由lindblad方程和线性增加的位点依赖性耗散的量子开放系统的框架中，我们公布了单个粒子相关函数的动态演化受假想史塔克梯子模型的汉密尔顿的控制。通过研究各个初始状态下密度分布的动力学演变，我们证明了阻尼动力学在不同区域显示出不同的行为。在强耗散极限中观察到局部阻尼。
We study an imaginary stark ladder model and propose a realization of the model in a dissipative chain with linearly increasing site-dependent dissipation strength. Due to the existence of a $K$-symmetry and passive $\mathcal{PT}$ symmetry, the model exhibits quite different feature from its Hermitian counterpart. With the increase of dissipation strength, the system first undergoes a passive $\mathcal{PT}$-symmetry breaking transition, with the shifted eigenvalues changing from real to complex, and then a $K$-symmetry restoring transition, characterized by the emergence of pure imaginary spectrum with equal spacing. Accordingly, the eigenstates change from $\mathcal{PT}$-unbroken extended states to the $\mathcal{PT}$-broken states, and finally to stark localized states. In the framework of the quantum open system governed by Lindblad equation with linearly increasing site-dependent dissipation, we unveil that the dynamical evolution of single particle correlation function is governed by the Hamiltonian of the imaginary stark ladder model. By studying the dynamical evolution of the density distribution under various initial states, we demonstrate that the damping dynamics displays distinct behaviors in different regions. A localized damping is observed in the strong dissipation limit.
