Chen Junbo, Zeng Jianhua
State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics of Chinese Academy of Sciences, Xi'an 710119, China.
Chaos. 2020 Jun;30(6):063131. doi: 10.1063/5.0006050.
Spontaneous symmetry breaking, a spontaneous course of breaking the spatial symmetry (parity) of the system, is known to exist in many branches of physics, including condensed-matter physics, high-energy physics, nonlinear optics, and Bose-Einstein condensates. In recent years, the spontaneous symmetry breaking of solitons in nonlinear wave systems is broadly studied; understanding such a phenomenon in nonlinear fractional quantum mechanics with space fractional derivatives (the purely nonlinear fractional systems whose fundamental properties are governed by a nonlinear fractional Schrödinger equation), however, remains pending. Here, we survey symmetry breaking of solitons in fractional systems (with the fractional diffraction order being formulated by the Lévy index α) of a nonlinear double-well structure and find several kinds of soliton families in the forms of symmetric and anti-symmetric soliton states as well as asymmetric states. Linear stability and dynamical properties of these soliton states are explored relying on linear-stability analysis and direct perturbed simulations, with which the existence and stability regions of all the soliton families in the respective physical parameter space are identified.
自发对称性破缺是指系统空间对称性（宇称）的自发破缺过程，已知在包括凝聚态物理、高能物理、非线性光学和玻色 - 爱因斯坦凝聚体在内的许多物理学分支中都存在。近年来，非线性波系统中孤子的自发对称性破缺得到了广泛研究；然而，对于具有空间分数阶导数的非线性分数量子力学（其基本性质由非线性分数薛定谔方程支配的纯非线性分数系统）中这种现象的理解仍有待解决。在此，我们研究了非线性双阱结构的分数系统（分数衍射阶由 Lévy 指数α表示）中孤子的对称性破缺，并发现了几种对称和反对称孤子态以及非对称态形式的孤子族。依靠线性稳定性分析和直接微扰模拟探索了这些孤子态的线性稳定性和动力学性质，借此确定了各个孤子族在相应物理参数空间中的存在和稳定区域。
