论文标题
拓扑定向放大
Topological directed amplification
论文作者
论文摘要
从理论上揭示了一种指向某些初始扰动的拓扑放大的现象，这些现象是在一类非正常toeplitz operators $ h_g $ $ h_g $带有积极的````$ h_g）（h_g g）> 0 $ $。非属性的偶然的偶然的均等的toeplitz操作员$ h_g $ $ h_g $ $ h_g $中出现的。边缘状态扩增的违反直觉瞬态 - 与渐近线大不相同的行为，$ h_g $的光谱分析无法直接揭示效果的一致描述。确定最佳初始条件的配方，该条件将通过传播器$ e^{ - i h_g t} $的单数值分解给出最大放大功率。进一步预测，皮肤效应激光阵列中非正态性与非线性之间的相互作用可以促进具有可扩展稳定输出功率的窄发射光谱。
A phenomenon of topological directed amplification of certain initial perturbations is revealed theoretically to emerge in a class of asymptotically stable skin-effect lattices described by nonnormal Toeplitz operators $H_g$ with positive ``numerical ordinate" $ω(H_g)>0$. Nonnormal temporal evolution, even in the presence of global dissipation, is shown to manifest a counterintuitive transient phase of edge-state amplification -- a behavior, drastically different from the asymptote, that spectral analysis of $H_g$ fails to directly reveal. A consistent description of the effect is provided by the general tool of ``pseudospectrum", and a quantitative estimation of the maximum power amplification is provided by the {\it Kreiss constant}. A recipe to determine an optimal initial condition that will attain maximum amplification power is given by singular value decomposition of the propagator $e^{-i H_g t}$. It is further predicted that the interplay between nonnormality and nonlinearity in a skin-effect laser array can facilitate narrow-emission spectra with scalable stable-output power.
