KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China.
Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Beijing 101408, China.
Chaos. 2023 Jan;33(1):013106. doi: 10.1063/5.0128910.
We report a novel spontaneous symmetry breaking phenomenon and ghost states existed in the framework of the fractional nonlinear Schrödinger equation with focusing saturable nonlinearity and PT-symmetric potential. The continuous asymmetric soliton branch bifurcates from the fundamental symmetric one as the power exceeds some critical value. Intriguingly, the symmetry of fundamental solitons is broken into two branches of asymmetry solitons (alias ghost states) with complex conjugate propagation constants, which is solely in fractional media. Besides, the dipole and tripole solitons (i.e., first and second excited states) are also studied numerically. Moreover, we analyze the influences of fractional Lévy index ( α) and saturable nonlinear parameters (S) on the symmetry breaking of solitons in detail. The stability of fundamental symmetric soliton, asymmetric, dipole, and tripole solitons is explored via the linear stability analysis and direct propagations. Moreover, we explore the elastic/semi-elastic collision phenomena between symmetric and asymmetric solitons. Meanwhile, we find the stable excitations from the fractional diffraction with saturation nonlinearity to integer-order diffraction with Kerr nonlinearity via the adiabatic excitations of parameters. These results will provide some theoretical basis for the study of spontaneous symmetry breaking phenomena and related physical experiments in the fractional media with PT-symmetric potentials.
我们在具有聚焦饱和非线性和 PT 对称势的分数阶非线性薛定谔方程框架中报告了一种新的自发对称破缺现象和鬼态。当功率超过某个临界值时，连续的不对称孤子分支从基本对称分支分叉出来。有趣的是，基本孤子的对称性被打破为具有复共轭传播常数的两个不对称孤子分支（别名鬼态），这仅在分数阶介质中存在。此外，还数值研究了偶极子和三极子孤子（即第一和第二激发态）。此外，我们详细分析了分数阶勒维指数（α）和饱和非线性参数（S）对孤子对称性破缺的影响。通过线性稳定性分析和直接传播，研究了基本对称孤子、不对称孤子、偶极子和三极子孤子的稳定性。此外，我们还研究了对称孤子和不对称孤子之间的弹性/半弹性碰撞现象。同时，我们通过参数的绝热激发，从具有饱和非线性的分数阶衍射到具有克尔非线性的整数阶衍射，找到了稳定的激发。这些结果将为分数阶介质中具有 PT 对称势的自发对称破缺现象和相关物理实验的研究提供一些理论依据。
