论文标题
双层孤子子在旋转轨道耦合的玻色 - 因子凝管中的自发对称性破坏
Spontaneous symmetry breaking of dual-layer solitons in spin-orbit-coupled Bose-Einstein condensates
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
It is known that stable 2D solitons of the semi-vortex (SV) and mixed-mode (MM) types are maintained by the interplay of the cubic attractive nonlinearity and spin-orbit coupling (SOC) in binary Bose-Einstein condensates. We introduce a double-layer system, in which two binary condensates, stabilized by the SOC, are linearly coupled by tunneling. By means of the numerical methods, it is found that symmetric two-layer solitons undergo the spontaneous-symmetry-breaking (SSB) bifurcation of the subcritical type. The bifurcation produces families of asymmetric 2D solitons, which exist up to the value of the total norm equal to the norm of the Townes solitons, above which the collapse occurs. This situation terminates at a critical value of the inter-layer coupling, beyond which the SSB bifurcation is absent, as the collapse sets in earlier. Symmetric 2D solitons that are destabilized by the SSB demonstrate dynamical symmetry breaking, in combination with intrinsic oscillations of the solitons, or transition to the collapse, if the soliton's norm is sufficiently large. Asymmetric MMs produced by the SSB instability start spontaneous drift, in addition to the intrinsic vibrations. Consideration of moving 2D solitons is a nontrivial problem because SOC breaks the Galilean invariance. It is found that the system supports moving MMs up to a critical value of the velocity, beyond which they undergo delocalization.
