论文标题
非线性系统的Bloch带结构和线性响应理论
Bloch band structures and linear response theory of nonlinear systems
论文作者
论文摘要
我们研究了BLOCH频段并为非线性系统开发了线性响应理论，其中拓扑参数和非线性之间的相互作用导致新的频带结构。正在考虑的非线性系统由具有Kerr型非线性的Qi-wu-zhang模型描述，可以将其视为Chern绝缘子的非线性版本。我们探索哈密顿量的特征力，并讨论其Bloch带结构以及差距闭合状况。发现了激发的Bloch带中的地面Bloch带和管结构的锥结构。我们还可以从数值计算非线性Chern绝缘子对外部场的线性响应，发现这些新的带结构破坏了绝热进化的条件，并使线性响应未量化。可以通过检查非线性系统的动力学来理解响应的这一特征。
We investigate the Bloch bands and develop a linear response theory for nonlinear systems, where the interplay between topological parameters and nonlinearity leads to new band structures. The nonlinear system under consideration is described by the Qi-Wu-Zhang model with Kerr-type nonlinearity, which can be treated as a nonlinear version of Chern insulator. We explore the eigenenergies of the Hamiltonian and discuss its Bloch band structures as well as the condition of gap closing. A cone structure in the ground Bloch band and tubed structure in the excited Bloch band is found. We also numerically calculate the linear response of the nonlinear Chern insulator to external fields, finding that these new band structures break the condition of adiabatic evolution and make the linear response not quantized. This feature of response can be understood by examining the dynamics of the nonlinear system.
