非线性调制声子晶格中依赖振幅的边缘态与离散呼吸子
Amplitude-dependent edge states and discrete breathers in nonlinear modulated phononic lattices
AI总结：
该研究探究一维空间调制非线性声子晶格的光谱特性随振幅的演化，揭示了边缘态的振幅依赖局域/退局域转变与振幅诱导的离散呼吸子生成现象，为相关态调控提供了新策略。
摘要：
我们研究了一维空间调制非线性声子晶格的光谱特性，以及它们随振幅的演化规律。在线性区域中，刚度调制定义了一族周期性和准周期性晶格，其带隙中存在局域在有限域边界处的拓扑边缘态。在三次非线性作用下，我们发现当振幅增加时，本征值分支仍保持在带隙内的边缘态会保持局域性，因此表现出对振幅的鲁棒性。相比之下，对应分支趋近于体带的边缘态会发生退局域化转变。这些转变通过对线性本征模随振幅变化的延拓研究得到预测，并通过有限晶格上的直接时域模拟得到证实。基于我们的预测，我们还观察到一系列振幅诱导的局域化转变：体模从非线性体带中脱离，成为局域在域内一个或多个区域的离散呼吸子。值得注意的是，这些预测的转变与有限晶格的尺寸无关，且在周期性和准周期性晶格中均存在。这些结果凸显了非线性调制晶格中拓扑边缘态与离散呼吸子的共存特性。二者的相互作用可被用于振幅诱导的本征态转变、评估局域态的鲁棒性，以及作为一种通过振幅调谐诱导离散呼吸子的策略。
英文摘要：
We investigate the spectral properties of one-dimensional spatially modulated nonlinear phononic lattices, and their evolution as a function of amplitude. In the linear regime, the stiffness modulations define a family of periodic and quasiperiodic lattices whose bandgaps host topological edge states localized at the boundaries of finite domains. With cubic nonlinearities, we show that edge states whose eigenvalue branch remains within the gap as amplitude increases remain localized, and therefore appear to be robust with respect to amplitude. In contrast, edge states whose corresponding branch approaches the bulk bands experience de-localization transitions. These transitions are predicted through continuation studies on the linear eigenmodes as a function of amplitude, and are confirmed by direct time domain simulations on finite lattices. Through our predictions, we also observe a series of amplitude-induced localization transitions as the bulk modes detach from the nonlinear bulk bands and become discrete breathers that are localized in one or more regions of the domain. Remarkably, the predicted transitions are independent of the size of the finite lattice, and exist for both periodic and quasiperiodic lattices. These results highlight the co-existence of topological edge states and discrete breathers in nonlinear modulated lattices. Their interplay may be exploited for amplitude-induced eigenstate transitions, for the assessment of the robustness of localized states, and as a strategy to induce discrete breathers through amplitude tuning.
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