论文标题
分级性的相互作用和$ \ cal {pt} $ - 对称在1D晶格上
Interplay of fractionality and $\cal{PT}$- symmetry on a 1D lattice
论文作者
论文摘要
我们在同时存在平等时间（$ \ cal {pt} $）对称性和分数的同时，检查了1D离散schrödinger方程的稳定域。对系统特征值的直接数值检查表明，随着部分指数从统一降低（标准情况），不稳定性增益突然超过了临界值。同样，随着系统的长度的增加，稳定的分数也减小。同样，对于固定的分数指数和晶格大小，增益/损失的增加也会导致不稳定性增益突然增加。最后，观察到模式的参与率随着增益/损耗参数的增加而降低，并减少了分数指数，从而证明了定位的趋势。
We examine the stability domains of a 1D discrete Schrödinger equation in the simultaneous presence of parity-time ($\cal{PT}$) symmetry and fractionality. Direct numerical examination of the eigenvalues of the system reveals that, as the fractional exponent is decreased away from unity (the standard case), the instability gain increases abruptly past a critical value. Also, as the length of the system increases, the stable fraction decreases as well. Also, for a fixed fractional exponent and lattice size, an increase in gain/loss also brings about an abrupt increase in the instability gain. Finally, the participation ratio of the modes is seen to decrease with an increase of the gain/loss parameter and with a decrease of the fractional exponent, evidencing a tendency towards localization.
