非线性PT对称低聚物中的非对称波传播
Asymmetric Wave Propagation Through Nonlinear PT-symmetric Oligomers
摘要：
在本文中，我们考虑非线性PT对称二聚体和三聚体（更一般地说，低聚物）嵌入在一个线性薛定谔晶格。我们研究了平面波形式的这种链的定态，并通过非线性PT对称低聚物解析计算其反射和透射系数，以及相应的整流因子，清楚地说明了在这种系统中左右传播之间的不对称性。我们不仅研究了平面波态的存在性，而且还研究了其动力学稳定性，有趣的是，我们发现它们是一般不稳定的。最后，我们将我们的数值考虑推广到更物理相关的高斯初始波包的情况下，并确认在这种波包的情况下，传输特性的不对称性仍然存在。
英文摘要：
In the present paper, we consider nonlinear PT-symmetric dimers and trimers (more generally, oligomers) embedded within a linear Schr{ö}dinger lattice. We examine the stationary states of such chains in the form of plane waves, and analytically compute their reflection and transmission coefficients through the nonlinear PT symmetric oligomer, as well as the corresponding rectification factors which clearly illustrate the asymmetry between left and right propagation in such systems. We examine not only the existence but also the dynamical stability of the plane wave states and interestingly find them to be generically unstable. Lastly, we generalize our numerical considerations to the more physically relevant case of Gaussian initial wavepackets and confirm that the asymmetry in the transmission properties persists in the case of such wavepackets, as well.
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